The generator matrix

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

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+104x^18+192x^19+401x^20+570x^21+662x^22+952x^23+1154x^24+1454x^25+1741x^26+1716x^27+1770x^28+1624x^29+1252x^30+1076x^31+671x^32+416x^33+306x^34+156x^35+93x^36+30x^37+30x^38+4x^39+6x^40+2x^41+1x^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 16.5 seconds.