The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1  X  1  X  1  1  X  1  1  X  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  0  0  X  X  X  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  0  0  X  X  0  0  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  X  X  0  0  X  X  X  X  0  X  0  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  0  X  0  0  X  0  X  0  X  0  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  0  X  0  X  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  0  X  X  0  0  X  X  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  0  0  X  X  0  0  0  X  X  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  0  0  0  X  X  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  0  X  X  X  0  0  X  0  X  X  X  X  X  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+150x^20+511x^24+128x^26+1221x^28+896x^30+2292x^32+896x^34+1397x^36+128x^38+437x^40+111x^44+23x^48+1x^52

The gray image is a linear code over GF(2) with n=64, k=13 and d=20.
This code was found by Heurico 1.16 in 77.5 seconds.