The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X X X^2 1 1 1 X X 1 X 1 0 1
0 X 0 X 0 0 X X^2+X 0 X^2 X X^2 X X X^2 0 X X X^2+X X^2+X X 0 0 0
0 0 X X 0 X^2+X X 0 X^2 X X X X X^2+X X^2+X 0 X^2+X X^2+X 0 0 X X^2 X 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0
0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0
0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2
0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2
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+43x^18+56x^19+96x^20+172x^21+212x^22+284x^23+330x^24+296x^25+218x^26+160x^27+70x^28+44x^29+36x^30+12x^31+13x^32+3x^34+2x^36
The gray image is a linear code over GF(2) with n=96, k=11 and d=36.
This code was found by Heurico 1.16 in 0.08 seconds.