The generator matrix

1 0 0 0 0 1 1 1 1 0 X 1 1 1 1 1 0 X X 0 1 1 X 1 X X 1 0 0 1 1 1
0 1 0 0 0 0 0 0 X X 0 1 1 X+1 1 X 1 1 1 X 0 1 X 1 1 1 0 1 X X+1 X 0
0 0 1 0 0 0 1 X 1 1 1 X+1 1 1 X X X 1 X+1 1 X+1 X 1 0 X 0 X 0 X X 0 1
0 0 0 1 0 1 X 0 1 X X+1 X X+1 X X X+1 1 1 0 1 0 X+1 0 0 X+1 1 X+1 X 1 1 X+1 0
0 0 0 0 1 X 0 1 1 X+1 1 X+1 X X 1 X+1 0 X 0 X X+1 0 X X X+1 1 X 1 X+1 0 X+1 X

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+38x^26+80x^27+104x^28+114x^29+91x^30+84x^31+70x^32+76x^33+80x^34+80x^35+64x^36+34x^37+43x^38+28x^39+15x^40+16x^41+4x^42+2x^44

The gray image is a linear code over GF(2) with n=64, k=10 and d=26.
This code was found by Heurico 1.10 in 0.032 seconds.