The generator matrix

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

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+56x^23+154x^24+246x^25+318x^26+424x^27+488x^28+546x^29+637x^30+754x^31+877x^32+762x^33+676x^34+626x^35+524x^36+434x^37+266x^38+174x^39+118x^40+56x^41+22x^42+14x^43+12x^44+4x^45+1x^46+2x^48

The gray image is a linear code over GF(2) with n=64, k=13 and d=23.
This code was found by Heurico 1.10 in 1.13 seconds.