The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  X  1  X  1  X  X  1  0  1  1  X  0  1  1  0  0
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  X  1  1 X+1  1  0  1  1 X+1  0  X  X  1  X  X  1  1  1
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  1  X  0  0  1 X+1  1  0  1 X+1  0  0  1 X+1 X+1 X+1  1
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0  1 X+1  X  X  1  X  0  0 X+1  0  1  1  1  1  0 X+1  0  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  0  X  X  0  0  0  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  0  X  X  X  0  X  0  X
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  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+76x^24+132x^25+180x^26+212x^27+251x^28+334x^29+317x^30+330x^31+358x^32+406x^33+363x^34+274x^35+300x^36+250x^37+136x^38+78x^39+36x^40+30x^41+24x^42+2x^43+1x^44+3x^46+1x^48+1x^50

The gray image is a linear code over GF(2) with n=64, k=12 and d=24.
This code was found by Heurico 1.16 in 0.836 seconds.