The generator matrix

 1  0  0  1  1  1 X^2+X  0  1  1 X^2 X^2+X  1  1 X^2  1  0 X^2+X  0  1 X^2+X  1  1  1  1  1  1
 0  1  0  0 X^2+1 X+1  1  X X+1 X^2+X  1  1  X X+1  1  1  1  1  1 X^2+X+1 X^2+X X^2+1 X^2+X X^2+X+1 X^2 X+1 X^2+1
 0  0  1  1  1 X^2  1  1 X^2+1  0 X^2 X^2+1 X^2+X+1  X X^2+1  0 X^2+X+1  1  X  X  1 X^2 X+1 X+1 X^2+X X^2+1 X^2+1
 0  0  0  X X^2+X  0  X  X X^2  X X^2+X  0 X^2  X  X X^2  X X^2 X^2  0 X^2+X  X  0 X^2 X^2 X^2+X 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+112x^23+295x^24+272x^25+232x^26+288x^27+267x^28+224x^29+152x^30+112x^31+68x^32+16x^33+9x^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 0.0784 seconds.