The generator matrix

1 0 0 0 0 1 1 1 X 1 1 0 1 X 1 X 0 1 1 0 X X 1 1 1 X 1 0 1
0 1 0 0 0 0 0 0 0 1 1 1 X X 1 0 X X+1 1 1 0 1 X X+1 X X 0 0 1
0 0 1 0 0 0 1 1 1 0 X X 0 X 1 1 X 1 X+1 1 1 X X+1 0 X 1 1 1 0
0 0 0 1 0 1 0 X+1 1 1 0 X+1 0 1 X 1 1 X+1 X 0 0 1 1 X X X+1 X+1 0 X+1
0 0 0 0 1 1 X+1 X 1 X 1 1 0 0 0 X+1 X X+1 1 0 X+1 0 1 X 1 X 0 X 0
0 0 0 0 0 X X 0 0 0 0 X X X X X 0 X 0 X 0 0 0 X X 0 0 0 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+48x^22+102x^23+107x^24+134x^25+191x^26+194x^27+182x^28+182x^29+164x^30+178x^31+169x^32+146x^33+100x^34+62x^35+46x^36+18x^37+8x^38+8x^39+7x^40+1x^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 1.10 in 0.078 seconds.