The generator matrix

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

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+88x^20+102x^21+228x^22+308x^23+418x^24+472x^25+606x^26+712x^27+675x^28+818x^29+762x^30+836x^31+626x^32+514x^33+377x^34+240x^35+217x^36+72x^37+69x^38+16x^39+23x^40+6x^41+5x^42+1x^46

The gray image is a linear code over GF(2) with n=58, k=13 and d=20.
This code was found by Heurico 1.10 in 0.922 seconds.