g23:=PermutationGroup< 351|(  1,213)(  2,235)(  3, 91)(  4,236)(  5,237)(  6, 87)(  7,238)(  8,170)(  9,177)
( 10,122)( 11, 13)( 12,239)( 14,183)( 15, 92)( 16,240)( 17,187)( 18, 25)( 19,241)
( 20,200)( 21, 74)( 22, 49)( 23,242)( 24,161)( 26,226)( 27,243)( 28, 57)( 29,228)
( 30,244)( 31,245)( 32,233)( 33,246)( 34,223)( 35,247)( 36,248)( 38,249)( 39,250)
( 40,251)( 41,151)( 42,206)( 43,209)( 44,252)( 46,121)( 47, 76)( 48,212)( 50,253)
( 51,137)( 52,254)( 53,255)( 54,256)( 55,145)( 56, 89)( 58,257)( 59,222)( 60,258)
( 61,107)( 62,217)( 63,259)( 64,101)( 65,202)( 66,260)( 67,224)( 69,261)( 70,188)
( 71,262)( 72,232)( 75,130)( 77,126)( 78,263)( 79,144)( 80,108)( 81,264)( 82,265)
( 83,184)( 84,102)( 85,266)( 86,136)( 88,143)( 90,267)( 95,268)( 96,269)( 97,270)
( 98,156)( 99,128)(100,271)(103,272)(104,168)(105,159)(106,129)(109,218)(110,273)
(111,181)(112,142)(113,274)(114,138)(116,275)(117,276)(118,277)(119,221)(120,210)
(123,278)(124,279)(125,197)(127,280)(131,189)(132,281)(133,158)(134,282)(135,141)
(139,283)(140,284)(146,190)(148,285)(149,286)(150,160)(152,287)(153,175)(154,180)
(155,288)(157,185)(162,289)(163,290)(164,291)(165,292)(166,293)(167,179)(169,294)
(171,295)(172,296)(174,204)(176,297)(178,298)(182,299)(186,300)(191,301)(192,230)
(193,302)(194,234)(195,303)(196,304)(198,305)(203,306)(205,307)(207,308)(208,309)
(211,227)(214,310)(215,311)(216,312)(219,229)(220,313)(225,314)(231,315)(316,336)
(317,349)(318,324)(320,338)(321,344)(322,330)(323,347)(325,340)(327,334)(328,329)
(331,343)(332,350)(333,351)(335,342)(337,341)(346,348), (  1, 89,316)(  2,127,317)(  3,255,  9)(  4,332,134)(  5,287,145)(  6,117,267)
(  7,320, 19)(  8,325, 84)( 10,243, 44)( 11,124,299)( 12,237,137)( 13,171,181)
( 14,155,177)( 15, 28,318)( 16,143,312)( 17,236, 66)( 18,183,319)( 20, 57,321)
( 21,130,322)( 22,123,253)( 23,151,168)( 24,277,148)( 25,106,207)( 26, 32,323)
( 27,334,178)( 29,162,246)( 30, 43,284)( 31,156,175)( 33,294, 87)( 34,313, 65)
( 35, 92,307)( 36,326, 85)( 37,250, 90)( 38,271,104)( 39,205, 82)( 40,200, 94)
( 41,290, 70)( 42,107,202)( 45,146,244)( 46,289,157)( 47,149,288)( 48,147,324)
( 49, 71,257)( 50,218,268)( 51, 78,311)( 52,262, 73)( 53,305,105)( 54,264,125)
( 55,113, 88)( 56,196,285)( 58,309, 77)( 59, 74,254)( 60,194,272)( 61,258,229)
( 62,220,297)( 63,278,233)( 64,275,222)( 67,286,142)( 68,132,295)( 69,179,266)
( 72,252,141)( 75,208,242)( 76,328,109)( 79,111, 83)( 80,304,232)( 81,223,217)
( 86,280,195)( 91,188,150)( 93,182,221)( 95,172,164)( 96,191,327)( 97,167,227)
( 98,260,121)( 99,173,215)(100,314,129)(101,180,166)(102,211,163)(103,333,140)
(108,235,116)(110,339,216)(112,306,122)(114,120,329)(115,159,330)(118,338,214)
(119,212,226)(126,193,161)(128,308,158)(131,153,331)(133,187,283)(135,154,169)
(136,310,186)(138,249,160)(139,240,228)(144,174,165)(152,213,301)(170,198,224)
(176,219,204)(184,210,335)(185,298,203)(189,199,336)(190,230,337)(192,225,263)
(197,231,300)(201,234,302)(206,256,209)(238,346,292)(239,265,340)(241,341,245)
(247,248,342)(251,281,274)(259,269,343)(261,296,344)(270,279,315)(273,347,293)
(276,291,345)(282,348,303)(349,350,351)>;
m1:=sub<g23 | (  2, 30)(  3,328)(  4,310)(  5,110)(  6, 35)(  7,260)(  8,150)(  9, 21)( 10,235)
( 12,308)( 13,176)( 14,224)( 17,331)( 18, 47)( 19, 56)( 20,345)( 22,344)( 23,263)
( 24,252)( 25,215)( 26,216)( 27, 98)( 28,326)( 29,291)( 31,336)( 32,324)( 33,250)
( 34,194)( 36,163)( 37, 95)( 38,102)( 39,287)( 40,318)( 41,305)( 42,219)( 43,225)
( 44,122)( 45, 60)( 46,243)( 48,261)( 49,201)( 50,276)( 52,309)( 54,280)( 55,162)
( 57,295)( 58,338)( 61, 81)( 62,238)( 63, 93)( 64,257)( 65,125)( 66,292)( 67,334)
( 68,315)( 70,279)( 71, 76)( 72,117)( 73,233)( 74,304)( 75,160)( 77,115)( 78,213)
( 79, 92)( 80,166)( 82,321)( 83,132)( 84, 90)( 85,184)( 86,144)( 87,273)( 88,181)
( 89,113)( 91,314)( 94,179)( 96,141)( 97,198)( 99,337)(100,155)(101,119)(103,107)
(104,158)(105,239)(108,169)(109,247)(111,320)(112,154)(114,142)(116,134)(118,317)
(120,255)(121,351)(123,242)(124,210)(126,316)(127,285)(128,143)(129,245)(130,180)
(131,152)(133,157)(135,139)(136,167)(137,251)(138,168)(140,348)(145,178)(146,206)
(147,182)(148,197)(149,172)(151,193)(153,301)(156,244)(159,254)(161,333)(164,227)
(165,202)(170,185)(171,212)(173,236)(174,329)(175,246)(177,306)(183,187)(186,341)
(188,319)(189,232)(190,346)(191,253)(192,265)(195,222)(196,327)(199,278)(200,312)
(203,343)(204,302)(207,311)(208,262)(209,270)(211,237)(214,303)(217,256)(218,323)
(220,297)(221,300)(223,284)(226,307)(228,347)(229,349)(231,313)(234,277)(240,332)
(241,259)(248,340)(249,268)(258,264)(266,299)(269,293)(271,335)(275,339)(282,350)
(283,289)(286,330)(288,325)(290,322)(294,298)(296,342), (2, 29)(3,286,158,139)
(4,191,129,192)(5,100,239, 40)(6, 96,214,296)(  7,175,137,173)(  8,106, 14,268)
(  9,160,155,179)( 10,305,246, 16)( 11,228,199,154)
( 12, 69,309, 41)( 13, 85, 57,248)( 15,135,201,111)( 17,122,141,252)( 18,215,189,128)
( 19,183, 27,350)( 20,324,342,167)( 21,108,259,257)( 22,273,147, 36)( 23,123,212,253)
( 24,150,345,143)( 25,102,319,121)( 26,274, 98,196)( 28, 95,339,265)( 30, 34,256,258)
( 31,270,267,157)( 32,153,103,125)( 33,213,242,109)( 35, 50, 38,314)( 37, 70,337,323)
( 39, 76)( 42,163,325,244)( 43,219,220,234)( 44,276,184,148)( 45,289,344,124)
( 46,144,200,237)( 47, 82,159, 75)( 48, 74, 97,181)( 49, 89,310, 73)( 51,266, 94,216)
( 52,316, 71,322)( 53,335,198,188)( 54,245,117,281)( 55,250,164,233)( 56,145,174,284)
( 58,177, 79,297)( 59,347,321,329)( 60,209,304,156)( 61,194,218,138)( 62,349,338,332)
( 63, 67,300,283)( 64,222,224, 91)( 65,302,336,295)( 66,112,208,346)( 68,307,327,241)
( 72,115,328,330)( 77,134,280,230)( 78,264,231,255)( 80, 86,225,142)( 81,116,193,186)
( 83,207,251,279)( 84, 92, 88,133)( 87,205,238,301)( 90,285,229,221)( 93,118,334,172)
( 99,290,113,132)(101,292,149,152)(104,272,320,140)(105,277,317,298)(107,195,206,303)
(110,178,211,282)(114,254,119,226)(120,227)(126,130,269,235)(127,210,243,312)
(131,190,202,299)(136,262,161,223)(146,187,176,165)(151,171,247,293)(162,203,275,185)
(166,294,288,306)(168,326)(169,340,271,331)(170,291)(180,236)(182,249,240,261)
(197,333,351,204)(232,278,318,315)(260,308,263,287)(311,348,313,341)>;
g:=m1;
a1,a2,a3:=CosetAction(g23,g);
st:=Stabilizer(a2,1);
orbs:=Orbits(st);#orbs;
v:=Index(a2,st);
v;
blox:=Setseq(orbs[2]^a2);
des:=Design<2,v|blox>;des;
au:=AutomorphismGroup(des);au;
p:=3;
dc:=descode(v,blox,p);
dl:=Dual(dc);
d1:=Dim(dc);d2:=Dim(dl);
d3:=Dim(dc meet dl); 
"p=",p,"dim=",d1,"dimdual=",d2,"hull=",d3;
pdc:=PermutationGroup(dc);#pdc;
cf:=CompositionFactors(pdc);cf;
re:=Residual(des, Block(des,351));
"res des =",re; 
are:=AutomorphismGroup(re);are;
cr:=CompositionFactors(are);cr;
cre:=LinearCode(re,GF(3));
"dimen code res des =",Dim(cre);
/* wre:=WD(cre);
"wdistr code res des =", wre;*/
pre:=PermutationGroup(cre);pre;
rf:=CompositionFactors(pre);rf;
dr:=Contraction(des,Block(des,351));
"deriv des",dr;
ade:=AutomorphismGroup(dr);ade;
cc:=CompositionFactors(ade);cc;
cd:=LinearCode(dr,GF(3));
"dimen code deriv =",Dim(cd);
pde:=PermutationGroup(cd);pde;
rfe:=CompositionFactors(pde);rfe;
/* wcd:=WD(cd);
"wdistr code deriv des =", wcd; */
cp:=Complement(des);
"compl des =",cp;
/* ccp:=LinearCode(cp,GF(3));
"dimen code compl=",Dim(ccp);
wcp:=WD(ccp);
"wdistr code compl =", wcp;
rre:=Residual(cp, Block(cp,351));
"res compl des =",rre; 
crre:=LinearCode(rre,GF(3));
"dimen code res comp des =",Dim(crre);
wrre:=WD(crre);
"wdistr code res comp des =", wrre;*/
ddr:=Contraction(cp,Block(cp,351));
"deriv compl des",ddr;
dec:=AutomorphismGroup(ddr);dec;
ce:=CompositionFactors(dec);ce;
ccd:=LinearCode(ddr,GF(3));
"dimen code deriv compl =",Dim(ccd);
pcd:=PermutationGroup(ccd);pcd;
rfd:=CompositionFactors(pcd);rfd;
/* wccd:=WD(ccd);
"wdistr code deriv compl des =", wccd;*/


=========== Output ==========

3
351
2-(351, 126, 45) Design with 351 blocks
Permutation group au acting on a set of cardinality 351
Order = 2^10 * 3^9 * 5 * 7 * 13
p= 3 dim= 27 dimdual= 324 hull= 27
9170703360
    G
    |  Cyclic(2)
    *
    |  B(3, 3)                = O(7, 3)
    1
res des = 2-(225, 81, 45) Design with 350 blocks
Permutation group are acting on a set of cardinality 225
Order = 26127360 = 2^10 * 3^6 * 5 * 7
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  2A(3, 3)               = U(4, 3)
    *
    |  Cyclic(2)
    1
dimen code res des = 26
Permutation group pre acting on a set of cardinality 225
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  2A(3, 3)               = U(4, 3)
    *
    |  Cyclic(2)
    1
deriv des Incidence Structure on 126 points with 350 blocks
Permutation group ade acting on a set of cardinality 476
Order = 2^121 * 3^6 * 5 * 7
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  2A(3, 3)               = U(4, 3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
dimen code deriv = 21
Permutation group pde acting on a set of cardinality 126
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  2A(3, 3)               = U(4, 3)
    1
compl des = 2-(351, 225, 144) Design with 351 blocks
deriv compl des 0-(225, 144, 350) Design with 350 blocks
Permutation group dec acting on a set of cardinality 225
Order = 26127360 = 2^10 * 3^6 * 5 * 7
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  2A(3, 3)               = U(4, 3)
    *
    |  Cyclic(2)
    1
dimen code deriv compl = 27
Permutation group pcd acting on a set of cardinality 225
    G
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  2A(3, 3)               = U(4, 3)
    *
    |  Cyclic(2)
    1