The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  X  1  1  1  X  1  0  1  1  1  1  1  0  0  1  0
 0  1  0  0  0  0  0  0  0  0  0  0  X  0  1  1  1  1  1  X X+1  X X+1  X  X  1  1  1  1
 0  0  1  0  0  0  0  0  X  X  1  1 X+1  1  1  1  X X+1  X  1 X+1  0  0  1  0  1 X+1  1  X
 0  0  0  1  0  0  X  1 X+1  1  0  1  1  1 X+1  0  1  0  X  X  1  0 X+1  0  1  X  X X+1  1
 0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  1  1  0 X+1 X+1  1  X  0  1  0 X+1  0 X+1  X X+1 X+1
 0  0  0  0  0  1  1  X  1  1 X+1  X  1  0  0  X X+1  X  X  X X+1  1  X  X  0  1 X+1 X+1  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+212x^22+484x^24+624x^26+680x^28+812x^30+641x^32+424x^34+175x^36+40x^38+2x^40+1x^52

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 0.798 seconds.