The generator matrix

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

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+154x^20+40x^22+695x^24+672x^26+2209x^28+2320x^30+4060x^32+2432x^34+2353x^36+648x^38+605x^40+32x^42+147x^44+15x^48+1x^52

The gray image is a linear code over GF(2) with n=64, k=14 and d=20.
This code was found by Heurico 1.16 in 11.4 seconds.