The generator matrix

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

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+68x^23+156x^24+226x^25+316x^26+414x^27+489x^28+550x^29+669x^30+812x^31+774x^32+696x^33+758x^34+680x^35+525x^36+376x^37+272x^38+192x^39+92x^40+70x^41+30x^42+10x^43+9x^44+2x^45+3x^46+1x^48+1x^52

The gray image is a linear code over GF(2) with n=64, k=13 and d=23.
This code was found by Heurico 1.16 in 3.37 seconds.