The generator matrix

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

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+49x^24+54x^25+90x^26+260x^27+145x^28+484x^29+156x^30+740x^31+167x^32+736x^33+155x^34+492x^35+116x^36+252x^37+82x^38+44x^39+31x^40+10x^41+26x^42+3x^44+2x^46+1x^50

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 0.445 seconds.