The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  1  X  X  1  1  0  1  1  0  0  1  0  X  0  X
 0  1  0  0  0  0  0  0  0 X+1  1  1 X+1  1 X+1  1  X X+1  0  1 X+1  0  X  1 X+1  1  1  1  0
 0  0  1  0  0  0  1  1  1  1  1  X  1  X  0  1  1  1  0  1  0 X+1  1 X+1  0  X  0  X  0
 0  0  0  1  0  1  1  0  1  0  X  X  1  1  0  0 X+1 X+1  0 X+1 X+1  X  X  X  X  0  1  X  1
 0  0  0  0  1  1  0  1  1 X+1  X  1  X  0  1 X+1  0  1 X+1  X X+1  X  1  1  0  1  X  X  X
 0  0  0  0  0  X  0  0  0  X  0  X  X  X  X  0  X  X  X  0  0  X  0  X  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  0  0  X  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  X  X  0  X  0  X  X  X  X  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  X  0  X  X  0  X  0  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+239x^20+744x^22+1527x^24+2334x^26+3339x^28+3188x^30+2634x^32+1504x^34+641x^36+164x^38+61x^40+2x^42+5x^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 18.9 seconds.