The generator matrix

 1  0  0  0  0  0  1  1  1  1  X  0  1  1  X  1  1  0  1  X  X  0  1  X  X  1  0
 0  1  0  0  0  0  0  0  0  0  0  1  1 X+1  X  1  X  1 X+1  0  X  1 X+1  X  X X+1  X
 0  0  1  0  0  0  0  0 X+1  1  1  0 X+1  X  0  X  1  1  X  X  1 X+1  X  1  0  0  1
 0  0  0  1  0  0  0  1  1  0 X+1  X X+1  X  0  0  1  0  1  1  X  1  0  1  1  1  1
 0  0  0  0  1  0  1  1  0 X+1  1 X+1  1  X  1 X+1  1  1  1  1 X+1  1  1  X X+1  1  X
 0  0  0  0  0  1  1  0 X+1  X X+1  1 X+1 X+1 X+1  0  0  0  X  X X+1  0  1  0  1  1  X
 0  0  0  0  0  0  X  0  X  0  X  X  X  X  X  X  X  X  0  X  0  X  X  0  0  X  X
 0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  0  X  0  0  X  0  X  X  X  X  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+131x^18+184x^19+361x^20+498x^21+765x^22+972x^23+1159x^24+1478x^25+1566x^26+1852x^27+1780x^28+1616x^29+1280x^30+964x^31+699x^32+456x^33+325x^34+124x^35+91x^36+46x^37+27x^38+5x^40+2x^41+2x^42

The gray image is a linear code over GF(2) with n=54, k=14 and d=18.
This code was found by Heurico 1.16 in 18.3 seconds.