The generator matrix

 1  0  0  0  1  1  1  1 X^2  1  0  X  1  1 X^2+X X^2 X^2  1 X^2+X  1  1 X^2  1  1
 0  1  0  0  0 X^2  1 X^2+1  1 X+1 X^2+X  1 X^2+1  X  1  1 X^2  X X^2+X X^2+X+1  1  X X^2+X+1  1
 0  0  1  0  0  1 X^2+1  X X+1  1  1 X^2 X^2+X  1 X+1  X X^2+X  X  1 X^2  1  1 X+1 X^2+X
 0  0  0  1 X+1 X+1 X^2  1  1  1 X^2+1 X^2+1 X^2+X X^2  X X^2+X+1  1 X^2+X+1 X^2  0 X^2+X X^2+X+1  0 X^2+1
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  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+220x^19+432x^20+706x^21+908x^22+1258x^23+1191x^24+1228x^25+906x^26+744x^27+339x^28+178x^29+56x^30+18x^31+4x^32+2x^34+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 1.16 in 0.7 seconds.