The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  X  1  1  1  0  X  1  0  X  1  0  1  0  0  0  X  0  1
 0  1  0  0  0  0  0  0  0  1  1  1  X  X X+1  1  X X+1  1  X X+1  X X+1  X  X  1  1  0  X
 0  0  1  0  0  0  1  1  1  1 X+1  0  0  1  X X+1  1 X+1 X+1  1  1  X X+1  1  0  X  1  X  0
 0  0  0  1  0  1  1  X X+1  0 X+1  1  X  X X+1 X+1  X  X  0  1 X+1  1  X  1  1  0  0  1  0
 0  0  0  0  1  1  X X+1  1  0  1  1  0  1  0  X  X  0 X+1 X+1  0 X+1  1  X  1 X+1  X  1  1
 0  0  0  0  0  X  0  X  0  X  0  0  X  0  0  X  X  0  0  X  X  0  X  0  X  X  X  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+38x^22+102x^23+132x^24+140x^25+156x^26+206x^27+190x^28+160x^29+198x^30+182x^31+145x^32+124x^33+106x^34+82x^35+42x^36+24x^37+12x^38+4x^39+2x^40+2x^42

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 0.178 seconds.