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^2  0  0  0  0 X^2 2X^2 2X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 2X^2 2X^2  0 X^2  0 X^2 X^2 2X^2 2X^2  0
 0  0 X^2  0  0 X^2 2X^2  0 2X^2  0 X^2 X^2 2X^2 2X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 2X^2 X^2  0  0 2X^2 X^2
 0  0  0 X^2  0 2X^2 2X^2 X^2  0 X^2 X^2  0  0 X^2 2X^2 X^2 X^2 2X^2  0 2X^2  0 2X^2  0 X^2 2X^2  0  0 2X^2 2X^2 X^2
 0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0  0 2X^2 2X^2  0 X^2 2X^2  0  0 2X^2 2X^2 X^2 2X^2  0 X^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+116x^54+1944x^60+88x^63+36x^72+2x^90

The gray image is a linear code over GF(3) with n=270, k=7 and d=162.
This code was found by Heurico 1.16 in 0.148 seconds.