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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+300x^54+598x^57+4972x^60+294x^63+284x^66+104x^69+6x^72+2x^90

The gray image is a linear code over GF(3) with n=270, k=8 and d=162.
This code was found by Heurico 1.16 in 0.106 seconds.