The generator matrix

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

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+186x^22+112x^23+453x^24+384x^25+664x^26+544x^27+651x^28+384x^29+418x^30+112x^31+130x^32+44x^34+13x^36

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 73.3 seconds.