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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+216x^103+144x^105+76x^108+270x^112+18x^132+4x^135

The gray image is a linear code over GF(3) with n=162, k=6 and d=103.
This code was found by Heurico 1.16 in 1.65 seconds.