The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+67x^22+132x^23+219x^24+298x^25+458x^26+484x^27+536x^28+704x^29+757x^30+816x^31+716x^32+764x^33+670x^34+520x^35+398x^36+256x^37+207x^38+92x^39+47x^40+26x^41+16x^42+4x^43+2x^44+1x^46+1x^48

The gray image is a linear code over GF(2) with n=62, k=13 and d=22.
This code was found by Heurico 1.16 in 3.13 seconds.