The generator matrix

1 0 0 0 1 1 1 1 1 X 1 1 X 0 1 1 1 1 0 1 1 X 1 1 1 1 1
0 1 0 0 0 0 1 1 X 1 X+1 X+1 X 1 X 0 1 1 1 X+1 1 0 0 X X 0 0
0 0 1 0 1 0 X 1 X+1 X+1 0 X 1 X+1 X+1 X+1 X+1 1 0 X 1 X X+1 1 0 0 0
0 0 0 1 1 X+1 X+1 X 0 1 0 X+1 X X 0 X+1 1 X X X 0 1 1 X 1 1 X+1
0 0 0 0 X X X 0 0 0 X 0 X X X 0 X X 0 X X X 0 0 0 X 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+30x^22+52x^23+54x^24+62x^25+58x^26+56x^27+47x^28+36x^29+23x^30+28x^31+19x^32+14x^33+16x^34+8x^35+7x^36+1x^38

The gray image is a linear code over GF(2) with n=54, k=9 and d=22.
This code was found by Heurico 1.10 in 0 seconds.