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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+56x^108+6x^110+6x^111+6x^113+6x^116

The gray image is a linear code over GF(3) with n=486, k=4 and d=324.
This code was found by Heurico 1.16 in 0.0423 seconds.