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

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+272x^54+486x^60+4374x^62+1252x^63+156x^72+18x^81+2x^90

The gray image is a linear code over GF(3) with n=279, k=8 and d=162.
This code was found by Heurico 1.16 in 76.6 seconds.