The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  0  X  X  X  0  0  0  0  X  X  X
 0  0  X  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  X  0
 0  0  0  X  0  0  0  X  0  X  X  0  0  0  X  X  0  X  X  0  0  X  X  0  0  X  X
 0  0  0  0  X  0  0  X  0  X  0  X  0  X  0  X  X  0  0  X  X  0  0  X  X  0  X
 0  0  0  0  0  X  0  X  X  0  0  X  0  X  X  0  0  0  X  X  X  0  X  0  X  0  0
 0  0  0  0  0  0  X  X  X  0  X  0  0  X  0  X  X  0  X  0  X  X  X  X  0  0  0

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+27x^22+36x^24+128x^27+36x^30+27x^32+1x^54

The gray image is a linear code over GF(2) with n=54, k=8 and d=22.
This code was found by Heurico 1.16 in 0.221 seconds.