The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+80x^26+44x^27+393x^28+260x^29+536x^30+472x^31+595x^32+456x^33+528x^34+252x^35+294x^36+52x^37+88x^38+28x^40+16x^42+1x^44

The gray image is a linear code over GF(2) with n=128, k=12 and d=52.
This code was found by Heurico 1.16 in 0.339 seconds.