The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1  X  0  1  0  1  1  1  1  0  X
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  0 X+1  1  X  1  X  1  0  1  1 X+1 X+1  X  X  1  0
 0  0  1  0  0  0  1  1  1  X  1 X+1 X+1 X+1 X+1 X+1  X  0  0  0  X  X X+1 X+1  1  0  0  0  1
 0  0  0  1  0  1  1  0 X+1  X  0  X X+1  X X+1  0  1  1 X+1 X+1  1  0  X  0  X  1  0  0  0
 0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  1 X+1  X X+1  0  0  0  0  1  1  1  1  1  1  1  1
 0  0  0  0  0  X  0  X  X  X  0  X  X  0  0  X  0  X  0  0  X  X  0  0  0  0  0  X  0
 0  0  0  0  0  0  X  0  X  0  X  X  0  X  X  0  X  X  0  X  0  X  X  0  0  0  X  0  0

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+216x^22+476x^24+604x^26+721x^28+814x^30+619x^32+434x^34+158x^36+42x^38+8x^40+2x^42+1x^44

The gray image is a linear code over GF(2) with n=58, k=12 and d=22.
This code was found by Heurico 1.16 in 1.17 seconds.