The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  0  0  1  X  1  X  1  0  1  1  1  1  0  1
 0  1  0  0  0  0  0  1  1  1 X+1 X+1  0  1  X  0  1  X  1  1  1  1  1  0  X  X X+1
 0  0  1  0  0  1  1  1  1  X  1  X  1  X  1 X+1 X+1  X X+1  1  X  X  0  1  X  0 X+1
 0  0  0  1  1  1  0  1  X X+1  1  0  1  1  X  1  X X+1  X  1 X+1  X  0  X  0  1  1
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  0  X  X  0  0  X  0
 0  0  0  0  0  X  0  0  X  0  X  X  0  0  0  X  0  X  X  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  0  0  X  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  0  0  0  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+195x^20+422x^22+657x^24+758x^26+824x^28+610x^30+460x^32+130x^34+37x^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 0.81 seconds.