The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  1  1  1  0  X  0  1  1  0  X  X  1  1  1  0  1
 0  1  0  0  0  0  0  0  1  1 X+1 X+1 X+1  X  0  1  1  1 X+1  X  1  1  1 X+1 X+1  1  0
 0  0  1  0  0  0  1  1  1  1  X X+1  X  1  1  X X+1  0  1  1  0  1  X  X X+1  1  0
 0  0  0  1  0  1  1  0  1  0 X+1  1  X  1 X+1  1  1  0  1  1  X  0  0  1  X X+1  0
 0  0  0  0  1  1  0  1  1  X X+1  X  0  1  0  X  X X+1  1  1  1  X  0  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  X  0  0  X  X  0  0  X  0  X  0  X  X  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  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+66x^18+84x^19+233x^20+272x^21+398x^22+510x^23+617x^24+650x^25+716x^26+978x^27+744x^28+778x^29+674x^30+534x^31+363x^32+206x^33+184x^34+66x^35+87x^36+14x^37+8x^38+4x^39+3x^40+2x^42

The gray image is a linear code over GF(2) with n=54, k=13 and d=18.
This code was found by Heurico 1.16 in 2.22 seconds.