The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  1  X  X  0  0  1  1  1  0  0  0  X  0  1  X  1  1
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1 X+1  X  1  1  X X+1  0  1  X  1  1  1  X X+1  X  1  0
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  0  1 X+1  1  0 X+1 X+1 X+1  1  0  1  0  1  0  X  1  0
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0  X  1 X+1  0  1  0 X+1  1  1  1  X  X  1 X+1  1  1  X
 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  X  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  0  0  X  X  X  0  X  X  X  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  0  X  X  0  X  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  0  0  X  0  X  0  X  X  X  X  0  0  0  0

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+56x^23+123x^24+168x^25+238x^26+276x^27+298x^28+320x^29+386x^30+388x^31+348x^32+368x^33+310x^34+252x^35+218x^36+160x^37+86x^38+52x^39+31x^40+8x^41+4x^42+4x^44+1x^48

The gray image is a linear code over GF(2) with n=62, k=12 and d=23.
This code was found by Heurico 1.16 in 1.46 seconds.