The generator matrix

 1  0  0  1  1  1  0  1  1  1  0  1  X  0  0  X  0  X  0  0  0  X  0  1  1  0  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  0  1  1  0  1  X  X  0  1  1  0  1  1  0
 0  0  1  1  1  0  1  0  1 X+1  0  X  1  1  0  1  1  X  1  1  1  1 X+1  0 X+1  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  X  X  0  0  X  X  X  0  0  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  0  X  0  0  X  X  0  0  X  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  0  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  0  X  X  0  0  X  X  X  X  X
 0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  X  0  0  0  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  0  X  0  0  X  X  X  0  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+27x^18+38x^19+92x^20+134x^21+183x^22+242x^23+283x^24+376x^25+414x^26+468x^27+461x^28+388x^29+318x^30+236x^31+161x^32+120x^33+71x^34+38x^35+22x^36+6x^37+11x^38+2x^39+3x^40+1x^44

The gray image is a linear code over GF(2) with n=54, k=12 and d=18.
This code was found by Heurico 1.16 in 0.558 seconds.