The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+918x^57+978x^58+1236x^59+3384x^60+1974x^61+2094x^62+3782x^63+1776x^64+1188x^65+1842x^66+444x^67+6x^68+30x^69+6x^70+12x^71+6x^72+6x^73

The gray image is a linear code over GF(3) with n=279, k=9 and d=171.
This code was found by Heurico 1.16 in 0.365 seconds.