The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  0  0  1  X  1  1  X  1  0  0  1  X  0  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  1  1 X+1  1  X X+1  X  1  0  X  1  X  1 X+1  X  0
 0  0  1  0  0  0  0 X+1  X  1  1  0  1  X  1  0  X  1 X+1  1  1 X+1  1  0  0  0  0
 0  0  0  1  0  0  0  1 X+1  1  0  1 X+1 X+1  X  1  0 X+1  X  X X+1  1  0  1  X  0  0
 0  0  0  0  1  0  1  0  1  1  1  X  X  1  1  X  1  0  0  1  0 X+1  1 X+1 X+1 X+1  0
 0  0  0  0  0  1  1 X+1  0 X+1  X X+1  0 X+1 X+1 X+1  X  X  1  X  1  X  X  1  1  0  0
 0  0  0  0  0  0  X  X  X  X  0  X  0  0  0  0  X  X  0  X  0  X  0  0  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+67x^18+70x^19+248x^20+288x^21+400x^22+500x^23+547x^24+710x^25+741x^26+900x^27+829x^28+804x^29+607x^30+520x^31+358x^32+232x^33+212x^34+54x^35+63x^36+12x^37+21x^38+4x^39+2x^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 1.16 in 2.39 seconds.