The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 0 X X^2 X X
0 X 0 0 0 0 0 0 0 X X^2+X X X^2 X^2 X 0 X^2 X^2+X X X 0 X X^2+X X^2
0 0 X 0 0 0 X X^2+X X X X 0 0 X X^2 X X^2+X X^2+X X^2 0 0 X X^2 X
0 0 0 X 0 X X X X^2 0 0 X^2 X^2 X^2 X^2+X X^2+X 0 X X^2+X X^2+X X X^2 0 0
0 0 0 0 X X X^2 X^2+X X^2+X 0 X X 0 X^2+X X X^2 X X^2+X X^2 X^2+X X X^2 0 X^2
0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 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+141x^18+8x^19+335x^20+128x^21+647x^22+336x^23+848x^24+448x^25+639x^26+104x^27+300x^28+137x^30+19x^32+4x^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 0.293 seconds.