The generator matrix

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

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+226x^22+124x^23+417x^24+388x^25+664x^26+536x^27+635x^28+360x^29+394x^30+108x^31+158x^32+20x^33+60x^34+5x^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 1.95 seconds.