The generator matrix

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

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+180x^22+316x^24+368x^26+376x^28+328x^30+275x^32+144x^34+56x^36+4x^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 1.16 in 0.553 seconds.