The generator matrix

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

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+89x^22+499x^24+735x^26+1272x^28+1370x^30+1693x^32+1258x^34+785x^36+361x^38+95x^40+23x^42+6x^44+4x^46+1x^52

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 9.6 seconds.