The generator matrix

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

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+60x^20+108x^21+212x^22+284x^23+404x^24+468x^25+557x^26+750x^27+760x^28+852x^29+864x^30+772x^31+631x^32+524x^33+362x^34+224x^35+168x^36+96x^37+52x^38+16x^39+20x^40+1x^42+2x^43+4x^44

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 2.71 seconds.