The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  1  0  1  1  1  1  0  1  X  X  0  X  1  X
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  X  1  1  0  X  1  X  0  1  X  1  1  X  1
 0  0  1  0  0  0  1  1  1  X  1 X+1 X+1  0  X  0 X+1  1  1  0  X  0  1  X  1  1 X+1
 0  0  0  1  0  1  1  0 X+1  X  0  X X+1  0  X  1  0 X+1 X+1  0  1  1  X  0  1 X+1  X
 0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  1 X+1 X+1  0  1  0  1  0  X  1  0  X X+1  X
 0  0  0  0  0  X  0  X  X  X  0  X  X  0  0  0  X  0  X  X  X  X  X  0  0  X  X
 0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  X  0  0  X  0  X  0  0  X  X  0  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+203x^20+396x^22+687x^24+740x^26+830x^28+628x^30+422x^32+156x^34+31x^36+1x^40+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 1.16 in 0.63 seconds.