The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1 X^2+X X^2  1  1  1 X^2+X  1  1  1  X  1 X^2  1  0  1  1
 0  1  1  0 X^2+X+1  1  X X^2+X+1  1  0 X+1  1  1 X^2+X+1  X  1  1 X^2  0 X^2+1  1 X^2+1  1 X^2  1 X^2+1  0
 0  0  X  0 X^2+X X^2  0  0 X^2+X X^2+X  X X^2+X X^2 X^2 X^2 X^2  X  X  X  X  0 X^2+X X^2 X^2+X X^2  0  0
 0  0  0  X  0 X^2 X^2+X  X X^2 X^2+X  X  X X^2+X X^2 X^2+X  0 X^2  0 X^2+X  X  X  X X^2+X  X  0  0  0
 0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 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+73x^22+60x^23+260x^24+224x^25+333x^26+200x^27+309x^28+224x^29+216x^30+60x^31+53x^32+17x^34+17x^36+1x^38

The gray image is a linear code over GF(2) with n=108, k=11 and d=44.
This code was found by Heurico 1.16 in 0.0728 seconds.