The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  0  X  1  1  1  X  1  1  X  X  0  X  1  X  X  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  0 X+1  0  0  X X+1 X+1  1  1  X  0 X+1  1  1  1
 0  0  1  0  1  1  0  1  0  1  1  X  0 X+1  1  X  0  1  1  1  1  1  0  1  1  X  1  X  0
 0  0  0  1  1  0  1  1  1  0 X+1  X  1  0  1  1  0 X+1  1  0 X+1  0  1 X+1  X  X X+1  1  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X  X  X  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  0  0  X  X  0  X  X  0  0  X  0  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  X  X  X  X
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  X  0  X  X  X  X  0  X  0  0  0  X  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  X  0  X  0  X  0  0  X  X  0  0  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+63x^20+86x^21+230x^22+292x^23+386x^24+494x^25+555x^26+716x^27+801x^28+880x^29+824x^30+772x^31+584x^32+512x^33+378x^34+260x^35+197x^36+74x^37+58x^38+8x^39+12x^40+2x^41+3x^42+3x^44+1x^48

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 2.77 seconds.