The generator matrix

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

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+128x^20+32x^21+72x^22+224x^23+137x^24+224x^25+48x^26+32x^27+104x^28+8x^30+13x^32+1x^40

The gray image is a linear code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0.453 seconds.