The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  0  0  X  0  0  X  0  X  1  X  1  X  X
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  1  1  1  1  0  X  0  1  0  1 X+1  1  0
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  0  X  1 X+1  1  1  1  1 X+1  X X+1  X  0
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  0  X  0  0  0  0  X  X  X  X  X
 0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  X  0  0  0  X  0  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  0  X  0  X  0  X  0  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  X  0  X  X  0  0  0  X  0
 0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  X  X  X  X  0  X  0  X  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+111x^20+166x^22+381x^24+366x^26+401x^28+306x^30+235x^32+58x^34+15x^36+7x^40+1x^44

The gray image is a linear code over GF(2) with n=54, k=11 and d=20.
This code was found by Heurico 1.16 in 0.163 seconds.