The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X X^2  0  1  X  1  1  X  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  0  0  X X^2  X  X X^2  0  0  X X^2 X^2+X  X  0
 0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X X^2  0  0  X X^2+X X^2+X  X X^2  0 X^2+X  0
 0  0  0  X  X  0  X X^2+X  0  X  X X^2 X^2 X^2+X X^2+X  X  0  0  0 X^2  X X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  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+34x^18+60x^19+92x^20+170x^21+258x^22+296x^23+274x^24+286x^25+240x^26+140x^27+72x^28+54x^29+42x^30+16x^31+9x^32+2x^33+2x^34

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 0.0787 seconds.