The generator matrix

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

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+28x^22+84x^23+188x^24+210x^25+343x^26+344x^27+436x^28+608x^29+658x^30+788x^31+761x^32+784x^33+671x^34+652x^35+524x^36+380x^37+300x^38+168x^39+120x^40+62x^41+41x^42+12x^43+16x^44+4x^45+6x^46+2x^48+1x^50

The gray image is a linear code over GF(2) with n=64, k=13 and d=22.
This code was found by Heurico 1.16 in 3.07 seconds.