The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+578x^108+126x^117+24x^126

The gray image is a linear code over GF(3) with n=165, k=6 and d=108.
As d=108 is an upper bound for linear (165,6,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.427 seconds.