The generator matrix

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

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+36x^20+84x^21+119x^22+146x^23+198x^24+182x^25+157x^26+222x^27+188x^28+170x^29+161x^30+126x^31+109x^32+74x^33+43x^34+18x^35+12x^36+2x^37

The gray image is a linear code over GF(2) with n=54, k=11 and d=20.
This code was found by Heurico 1.10 in 0.047 seconds.