The generator matrix

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

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+60x^23+148x^24+226x^25+346x^26+392x^27+513x^28+596x^29+634x^30+772x^31+755x^32+744x^33+748x^34+636x^35+514x^36+428x^37+281x^38+176x^39+112x^40+54x^41+34x^42+12x^43+5x^44+4x^46+1x^54

The gray image is a linear code over GF(2) with n=64, k=13 and d=23.
This code was found by Heurico 1.16 in 4.21 seconds.