The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+59x^20+76x^21+141x^22+240x^23+294x^24+330x^25+321x^26+368x^27+383x^28+406x^29+385x^30+340x^31+269x^32+198x^33+135x^34+72x^35+49x^36+14x^37+10x^38+4x^39+1x^44

The gray image is a linear code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.10 in 0.25 seconds.