The generator matrix

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

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+46x^22+72x^23+151x^24+154x^25+172x^26+194x^27+144x^28+206x^29+159x^30+182x^31+168x^32+134x^33+119x^34+62x^35+43x^36+18x^37+15x^38+2x^39+4x^40+1x^42+1x^44

The gray image is a linear code over GF(2) with n=58, k=11 and d=22.
This code was found by Heurico 1.16 in 0.179 seconds.