The generator matrix

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

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+73x^20+38x^22+289x^24+228x^26+417x^28+336x^30+329x^32+156x^34+148x^36+10x^38+21x^40+1x^44+1x^52

The gray image is a linear code over GF(2) with n=58, k=11 and d=20.
This code was found by Heurico 1.16 in 0.183 seconds.