The generator matrix

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

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+92x^18+72x^19+230x^20+292x^21+375x^22+506x^23+568x^24+676x^25+721x^26+914x^27+807x^28+826x^29+647x^30+494x^31+382x^32+242x^33+199x^34+62x^35+55x^36+10x^37+14x^38+5x^40+2x^41

The gray image is a linear code over GF(2) with n=54, k=13 and d=18.
This code was found by Heurico 1.10 in 0.796 seconds.