The generator matrix

 1  0  0  1  1  1  0  1  1  1  0  1  X  0  1  1  0  0  X  1  1  0  X  1  X  1  1  0  1
 0  1  0  1  0  1  1  0  0  1  1 X+1  1  0  0  X  0  1  1 X+1  1  0  1  1  1 X+1  1  1  X
 0  0  1  1  1  0  1  0  1  1  X  0 X+1  1  0  1  1  0  1  X  1  1  1 X+1 X+1  0  1  X  1
 0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  0  0  0  0  X  0  X  X  X  X  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  0  0  X  X  0  X  X  0  0  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  X  0  X  X  0  0  0  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  0  X  0  X  0  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  X  0  0  0  X  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  0  X  0  0  X  0  X  0  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+165x^20+272x^22+798x^24+1096x^26+1833x^28+1544x^30+1391x^32+600x^34+367x^36+72x^38+50x^40+3x^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 2.45 seconds.