The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  0  1  0  0  1  1  X  1  0  1  0
 0  1  1  0  1  1  0  1  1  X X+1  1  0 X+1  1  0  1 X+1  1  1  0 X+1  1  0  1 X+1  X
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  X  X  0  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  X  0  X  X  X  0  X
 0  0  0  0  X  0  0  0  0  0  X  0  X  0  0  X  X  X  X  0  0  X  0  X  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  X  0  0  X  0  0  0  0  X  X  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  X  0  X  0  X  0  X  X  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  0  0  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  0  X  0  0  X  0  0  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+135x^20+128x^22+371x^24+352x^26+496x^28+256x^30+233x^32+32x^34+39x^36+3x^40+2x^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 0.635 seconds.