The generator matrix

 1  0  0  0  0  0  1  1  1  1  0  1  1  1  1  X  1  1  0  1  0  X  0  X  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  1 X+1  1  X  1  X  1  1  X  1  X X+1 X+1  1  1  0
 0  0  1  0  0  0  0 X+1  0  1  1  X X+1  1  1  1  1  X  X  0  1  1 X+1  1  0  X X+1  0  0
 0  0  0  1  0  0  0  1  1  X  1 X+1  1  X  1  0  1  1  1  0  X  1  1  0  X  0  0  X  0
 0  0  0  0  1  0  1  0 X+1  1 X+1  X  1  1  X  1 X+1  X  0 X+1  X  X  1  X  X  0 X+1  X  0
 0  0  0  0  0  1  1 X+1  X  X  1 X+1 X+1 X+1  0  1  X  1 X+1  0  1 X+1  1 X+1 X+1  0  X  1  0
 0  0  0  0  0  0  X  X  0  0  X  0  0  X  X  0  X  X  X  X  0  0  X  X  X  0  X  X  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+98x^20+72x^21+274x^22+280x^23+424x^24+494x^25+530x^26+744x^27+667x^28+878x^29+734x^30+820x^31+650x^32+478x^33+417x^34+256x^35+183x^36+58x^37+83x^38+12x^39+25x^40+4x^41+9x^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 1.16 in 2.75 seconds.