The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+234x^19+405x^20+796x^21+690x^22+1514x^23+878x^24+1560x^25+772x^26+814x^27+246x^28+172x^29+74x^30+30x^31+5x^32+1x^36

The gray image is a linear code over GF(2) with n=96, k=13 and d=38.
This code was found by Heurico 1.11 in 0.281 seconds.