The generator matrix

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

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+202x^22+497x^24+624x^26+718x^28+740x^30+653x^32+448x^34+177x^36+34x^38+1x^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 1.10 in 0.375 seconds.