The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+393x^20+244x^21+732x^22+256x^23+795x^24+328x^25+816x^26+160x^27+305x^28+36x^29+20x^30+8x^32+2x^36

The gray image is a linear code over GF(2) with n=96, k=12 and d=40.
This code was found by Heurico 1.16 in 0.459 seconds.