The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  0  X  1  1  1  1  1  1  1  1  X  1  0  1
 0  1  0  1  0  1  1  0  0  1 X+1  1  1  0  X  1  1  1  X  1  1  1 X+1 X+1  0  1 X+1  0  0
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  1  0  X  1 X+1  1  1 X+1 X+1  1  0  1  0  1  0
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  0  0  X  X  X  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  0  X  X  X  0  0  X  0  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0  0  X  X  0  0  X  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  X  0  X  0  0  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  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+48x^20+52x^21+97x^22+96x^23+254x^24+304x^25+292x^26+288x^27+336x^28+568x^29+336x^30+288x^31+287x^32+304x^33+248x^34+96x^35+96x^36+52x^37+46x^38+2x^40+4x^42+1x^54

The gray image is a linear code over GF(2) with n=58, k=12 and d=20.
This code was found by Heurico 1.16 in 0.645 seconds.