The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  X  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  X  0  X  X  X  X  X  0  0  0  X
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  0  X  0  0  0  X  0  0  X  0  X
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  X  X  0  0  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  0  X  0  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  0  X  0  X  X  X  X  X  X  X
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  X  X  X  0  X  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  X  0  X  0  0  0  0  X  X  0

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+81x^24+8x^26+166x^28+120x^30+279x^32+120x^34+161x^36+8x^38+69x^40+8x^44+2x^48+1x^52

The gray image is a linear code over GF(2) with n=64, k=10 and d=24.
This code was found by Heurico 1.16 in 0.0855 seconds.