The generator matrix

1 0 0 0 0 1 1 1 X 1 1 1 0 1 0 1 X X 1 1 0 1 X 1 1 0 0 1
0 1 0 0 0 0 0 X X 1 1 X+1 X X 0 X+1 1 1 X X 1 X+1 0 1 1 X 1 0
0 0 1 0 0 1 X 1 1 0 X+1 0 X 1 1 X+1 X 1 0 X 1 X 1 1 0 0 1 X
0 0 0 1 0 1 X+1 0 1 X X+1 1 1 X+1 X 0 X 1 X 1 X+1 X X+1 X 0 1 X+1 1
0 0 0 0 1 X 1 1 X+1 1 X+1 X+1 X+1 X+1 X+1 X+1 1 1 0 0 0 X X X+1 1 1 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+28x^22+82x^23+95x^24+98x^25+104x^26+90x^27+74x^28+90x^29+91x^30+72x^31+74x^32+46x^33+30x^34+26x^35+12x^36+6x^37+3x^38+2x^39

The gray image is a linear code over GF(2) with n=56, k=10 and d=22.
This code was found by Heurico 1.10 in 0.016 seconds.