The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  X X^2  0  0  1  1  1  0 X^2+X  1  1  1  1  1
 0  1  0  1  0 X^2+X+1  1  1 X^2  X  0  1  1  1  1 X^2+X X^2+X+1  1  1 X^2+X  0 X+1  1  0
 0  0  1  1  1  0  1  1  0 X^2+1  1 X^2+X+1  X X^2+X X^2 X^2+X+1 X^2+1 X+1  0 X+1 X^2 X^2+X+1  1  0
 0  0  0  X  0  0  0 X^2  X  X X^2+X X^2 X^2+X  0 X^2  X  X X^2 X^2+X X^2+X  X X^2  0  0
 0  0  0  0  X X^2+X X^2+X  0 X^2  X X^2 X^2+X X^2  X X^2  0 X^2+X  0 X^2+X  X X^2+X 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+45x^18+230x^19+344x^20+664x^21+948x^22+1136x^23+1416x^24+1214x^25+994x^26+630x^27+272x^28+196x^29+60x^30+20x^31+15x^32+6x^33+1x^34

The gray image is a linear code over GF(2) with n=96, k=13 and d=36.
This code was found by Heurico 1.16 in 0.854 seconds.