The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+152x^23+195x^24+324x^25+206x^26+364x^27+229x^28+288x^29+68x^30+120x^31+52x^32+28x^33+14x^34+4x^35+3x^36

The gray image is a linear code over GF(2) with n=108, k=11 and d=46.
This code was found by Heurico 1.16 in 0.0621 seconds.