The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+34x^19+110x^20+200x^21+319x^22+404x^23+491x^24+544x^25+686x^26+792x^27+819x^28+876x^29+780x^30+726x^31+528x^32+328x^33+245x^34+148x^35+91x^36+36x^37+16x^38+6x^39+8x^40+1x^42+2x^43+1x^46

The gray image is a linear code over GF(2) with n=56, k=13 and d=19.
This code was found by Heurico 1.10 in 0.875 seconds.