The generator matrix
1 0 0 1 1 1 X^2+X 1 1 1 X X^2+X 1 0 X 1 1 1 1 1 X 1 0 X
0 1 0 1 0 1 1 X 1 X 1 1 X+1 X 1 0 0 X^2+X+1 X^2+X+1 X^2+X X^2 0 0 X^2
0 0 1 1 1 0 1 X+1 1 X X^2+X X^2+1 X 1 X X^2+X+1 X^2 X X 0 1 X^2 1 X
0 0 0 X 0 0 0 0 0 0 0 X^2 X^2 X X^2+X X X^2+X X X X^2 X 0 X^2 X
0 0 0 0 X 0 0 0 X^2 X X X^2+X X^2+X X^2+X X^2 0 0 X X^2 X^2+X 0 X X X^2+X
0 0 0 0 0 X X^2+X X^2+X 0 X X^2+X 0 X^2 X^2+X X^2 X X^2 0 X^2+X 0 X X X^2+X 0
generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.
Homogenous weight enumerator: w(x)=1x^0+120x^17+383x^18+742x^19+1366x^20+2482x^21+3699x^22+4778x^23+5486x^24+4942x^25+3711x^26+2506x^27+1389x^28+702x^29+301x^30+102x^31+45x^32+10x^33+2x^34+1x^44
The gray image is a linear code over GF(2) with n=96, k=15 and d=34.
This code was found by Heurico 1.16 in 21 seconds.