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.