The generator matrix
1 0 1 1 1 X^2+X 1 X^2 1 0 1 1 X 1 X^2 1 X 1 X^2+X 1 1 1 X^2+X 1
0 1 1 0 X^2+X+1 1 X 1 X+1 1 0 1 1 X 1 X^2 1 X+1 1 X^2+X 1 X^2+1 1 0
0 0 X 0 X^2+X 0 0 X^2 X X X^2+X X^2 X X^2+X X^2+X X^2+X X X^2 X X X^2 X^2+X X^2+X 0
0 0 0 X 0 0 X^2+X X^2+X X X X X^2+X X^2 X^2 0 X^2 X^2 X^2 X X^2+X X^2+X X^2+X X 0
0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0
0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 0
generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+41x^18+122x^19+141x^20+398x^21+346x^22+764x^23+492x^24+768x^25+340x^26+386x^27+122x^28+110x^29+38x^30+8x^31+11x^32+4x^33+3x^34+1x^36
The gray image is a linear code over GF(2) with n=96, k=12 and d=36.
This code was found by Heurico 1.16 in 0.209 seconds.