The generator matrix

 1  0  0  1  1  1  X  X  1  1  1  0  1  1  X  1  1  1  1 X^2  1 X^2  1  1 X^2+X  X X^2
 0  1  0  0  1  1  1  1 X+1  X  1  1  X X^2  0  X X+1 X^2 X+1  1  0  X  X  1  1 X^2+X  1
 0  0  1 X+1 X^2+X+1  0  1  X X^2+X+1  1  X X^2+X+1  X  1  1 X+1 X+1  X X^2  X  1  1  X X+1 X^2+1  1  X
 0  0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+122x^22+216x^23+394x^24+520x^25+523x^26+608x^27+524x^28+480x^29+349x^30+200x^31+97x^32+24x^33+29x^34+8x^36+1x^38

The gray image is a linear code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 0.22 seconds.