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.