The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  0  X  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0  X  0  X  X  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  0  X  X  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  X  X  X  0  0  0  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  0  0  X  0  X  X  X  0  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  0  0  X  X  X  X  0  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  X  X  0  X  X  0  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  0  X  0  X  0  0  X  X  X  X  0  0  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+66x^22+118x^24+104x^26+120x^28+103x^30+1024x^31+103x^32+120x^34+104x^36+118x^38+66x^40+1x^62

The gray image is a linear code over GF(2) with n=62, k=11 and d=22.
This code was found by Heurico 1.16 in 26.5 seconds.