The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  1  X  X  X  X  0  0  1  1  1  1  0  X  X  X  0  1
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  X  1  0  1  1  0  1  1  0 X+1  1  1  1  0  1  X  X
 0  0  1  0  1  1  0  1  0  1  1  0  1  0  1  1  1  X  1  X X+1  0 X+1 X+1  X  1  1  1  1
 0  0  0  1  1  0  1  1  1  0  1  0 X+1  1  1  0 X+1  1  1  1  0  0  1  X  X  X  X X+1 X+1
 0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  0  0  0  X  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  X  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  X  0  0  X  0  0  X  X  0  X  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  0  X  X  0  X  X  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  X  X  0  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  0  X  X  X  X  X  X  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+312x^20+628x^22+1494x^24+2374x^26+3420x^28+3152x^30+2721x^32+1348x^34+696x^36+172x^38+54x^40+6x^42+4x^44+2x^48

The gray image is a linear code over GF(2) with n=58, k=14 and d=20.
This code was found by Heurico 1.16 in 51.9 seconds.