The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+48x^18+130x^19+258x^20+422x^21+535x^22+750x^23+945x^24+1142x^25+1398x^26+1538x^27+1689x^28+1760x^29+1597x^30+1262x^31+970x^32+716x^33+459x^34+316x^35+217x^36+114x^37+56x^38+36x^39+16x^40+6x^41+3x^42

The gray image is a linear code over GF(2) with n=56, k=14 and d=18.
This code was found by Heurico 1.10 in 3.08 seconds.