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

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+32x^17+93x^18+224x^19+329x^20+498x^21+735x^22+930x^23+1272x^24+1462x^25+1575x^26+1770x^27+1798x^28+1610x^29+1270x^30+1006x^31+735x^32+450x^33+275x^34+158x^35+89x^36+44x^37+19x^38+8x^39+1x^42

The gray image is a linear code over GF(2) with n=54, k=14 and d=17.
This code was found by Heurico 1.10 in 2.89 seconds.