The generator matrix

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

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+161x^22+166x^24+220x^26+170x^28+150x^30+97x^32+44x^34+14x^36+1x^38

The gray image is a linear code over GF(2) with n=54, k=10 and d=22.
This code was found by Heurico 1.16 in 0.773 seconds.