The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  1  1  1  X  0  1  1  1  0  1  1  0  0  0  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X X+1 X+1  1  1 X+1 X+1  1  1  1 X+1  1
 0  0  1  0  0  0  0  0 X+1  0  1  1  X  X X+1  X  1  1 X+1  1 X+1  1 X+1  0 X+1  X  0  X  1
 0  0  0  1  0  0  0  1  1  1  1  0  X  1 X+1  1  X X+1  0  X  1 X+1 X+1 X+1  0  1  X  1  1
 0  0  0  0  1  0  1  1  0 X+1  0  0  X  0 X+1 X+1 X+1  0 X+1  1  1 X+1  X  1 X+1  0 X+1 X+1  1
 0  0  0  0  0  1  1  0 X+1 X+1  X X+1  1  0  1  1 X+1 X+1  0  1  X  X X+1  0 X+1  X  1  X  0
 0  0  0  0  0  0  X  0  X  X  0  X  0  X  0  0  0  X  X  0  0  X  X  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  0  0  X  X  0  X  0  X  0  X  X  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+251x^20+710x^22+1553x^24+2368x^26+3207x^28+3340x^30+2622x^32+1432x^34+637x^36+206x^38+47x^40+8x^42+1x^44+1x^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 20.7 seconds.