The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  0  X  X  X  X  0  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  0  0  0  X  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  X  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  X  0  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  0  X  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  X  0  0  X  0  0  0  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  0  X  X  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+26x^20+40x^22+74x^24+55x^26+128x^27+60x^28+256x^29+62x^30+128x^31+63x^32+70x^34+26x^36+25x^38+6x^40+3x^42+1x^54

The gray image is a linear code over GF(2) with n=58, k=10 and d=20.
This code was found by Heurico 1.16 in 0.0629 seconds.