The generator matrix

 1  0  0  1  1  1  X  0  1  1  1  1  X  0  1  1  1  1  1  X  1  1  X  1  X  X  1
 0  1  0  1  0  1  1  1  0 X+1  X X+1  X  1 X+1 X+1  0 X+1  1  1  0  1  1 X+1  1  1  X
 0  0  1  1  1  0  1  X  0  0 X+1  1  1 X+1  0  X  0  X  1  X  X  X  X X+1  0  0  1
 0  0  0  X  0  0  0  X  X  0  0  0  X  0  X  X  X  0  X  0  0  X  X  0  0  0  X
 0  0  0  0  X  0  0  X  X  X  0  0  0  X  X  0  0  X  X  0  X  X  X  X  X  X  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  X  0  X  X  X  0  X  X  X  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+23x^22+60x^23+59x^24+62x^25+61x^26+50x^27+41x^28+20x^29+33x^30+40x^31+20x^32+14x^33+11x^34+10x^35+7x^36

The gray image is a linear code over GF(2) with n=54, k=9 and d=22.
This code was found by Heurico 1.16 in 0.0141 seconds.