The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+192x^22+303x^24+346x^26+381x^28+376x^30+256x^32+130x^34+51x^36+12x^38

The gray image is a linear code over GF(2) with n=56, k=11 and d=22.
This code was found by Heurico 1.10 in 0.219 seconds.