The generator matrix

 1  0  0  0  0  1  1  1  1  1  1 X^2  X  1 X^2  1  1  1  X X^2  1  0  X  X
 0  1  0  0  0 X^2 X^2  0  0  0 X^2+1  1  1 X^2+X+1  1 X^2+X X^2+X X^2+1 X^2+X  1 X^2+1 X^2+X  X  1
 0  0  1  0  0 X^2  0 X^2+1 X+1 X^2+X+1 X^2  X X+1 X^2+1  1  1  X  0 X^2 X^2+X X^2+X+1  1  1  1
 0  0  0  1  0  1  X  X X^2+X X+1 X^2 X^2+1 X+1  0  X  1 X^2+1 X+1 X^2+X  0 X^2+X X^2 X^2+X+1  1
 0  0  0  0  1  1 X+1 X^2+1  X X+1 X^2+X+1 X^2+1 X^2+X+1  X X^2  0  X X^2+X  1 X^2+1  1  X  0  1

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+326x^18+756x^19+1593x^20+2388x^21+4036x^22+4348x^23+5439x^24+4892x^25+4166x^26+2348x^27+1535x^28+524x^29+272x^30+100x^31+40x^32+4x^33

The gray image is a linear code over GF(2) with n=96, k=15 and d=36.
This code was found by Heurico 1.13 in 3.66 seconds.