The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 X 1 1 1 1 1 X 1 X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X 0 X X X X X X 0 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 0 0 X 0 X 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X X 0 X 0 X 0 X X X 0 X X 0 X X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X X X 0 X 0 0 X 0 0 X X 0 X 0 X X X 0
0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 0 X X 0 X X 0 0 0 X 0 0 X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X X X X X X 0 X X 0 0 0 0 0 X X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X X 0 0 0 0 X 0 X X X 0 X 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X 0 0 X X X X 0 X 0 0 X 0 0 0 X X
0 0 0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X 0 X 0 X 0 0 0 0 X X X X 0
0 0 0 0 0 0 0 0 0 0 X X X 0 0 X 0 X 0 0 X X X 0 X X X 0 X 0 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+48x^20+55x^22+160x^24+146x^26+64x^27+206x^28+320x^29+215x^30+640x^31+307x^32+640x^33+320x^34+320x^35+204x^36+64x^37+191x^38+76x^40+74x^42+22x^44+17x^46+4x^50+2x^54
The gray image is a linear code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 1.03 seconds.