The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  X  1  1  0  X  0  1  X  X  X  1  X  1  1  1  X
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  1  0  X  0  X  X  1  0  0 X+1  1  1  1 X+1  1  0  1  1  1
 0  0  1  0  1  1  0  1  0  1  1  0  1  0  1 X+1  1  1  0  X  1  X  1  X X+1  1  1  0  X X+1  0  1
 0  0  0  1  1  0  1  1  1  0  1  0  0  1  1  X X+1 X+1 X+1 X+1  X  1  0  0  X  0  1  0  X  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  X  X  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  X  X  X  0  X  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  0  0  0  X  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  0  X  0  X  0  0  X  0  X  0  0  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  0  X  X  0  0  0  0  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  X  0  0  X  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+142x^22+564x^24+1084x^26+1902x^28+2744x^30+3301x^32+3032x^34+1980x^36+1022x^38+404x^40+156x^42+38x^44+12x^46+2x^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 26.8 seconds.