The generator matrix

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

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+168x^20+484x^22+644x^24+716x^26+822x^28+640x^30+450x^32+140x^34+26x^36+4x^38+1x^48

The gray image is a linear code over GF(2) with n=54, k=12 and d=20.
This code was found by Heurico 1.10 in 0.312 seconds.