The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+416x^108+134x^111+154x^114+18x^117+4x^120+2x^123

The gray image is a linear code over GF(3) with n=495, k=6 and d=324.
This code was found by Heurico 1.16 in 4.87 seconds.