The generator matrix

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

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+91x^22+116x^23+309x^24+428x^25+573x^26+696x^27+966x^28+1188x^29+1388x^30+1596x^31+1524x^32+1652x^33+1386x^34+1380x^35+1028x^36+708x^37+563x^38+288x^39+243x^40+112x^41+89x^42+20x^43+22x^44+8x^45+6x^46+3x^48

The gray image is a linear code over GF(2) with n=64, k=14 and d=22.
This code was found by Heurico 1.16 in 22.7 seconds.