The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+30x^54+58x^57+220x^60+1458x^62+354x^63+14x^66+8x^69+18x^72+18x^75+6x^78+2x^90

The gray image is a linear code over GF(3) with n=279, k=7 and d=162.
This code was found by Heurico 1.16 in 0.0236 seconds.