The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+82x^24+96x^26+32x^27+318x^28+288x^29+288x^30+704x^31+500x^32+704x^33+288x^34+288x^35+289x^36+32x^37+96x^38+72x^40+16x^44+1x^48+1x^52

The gray image is a linear code over GF(2) with n=128, k=12 and d=48.
This code was found by Heurico 1.16 in 0.488 seconds.