The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+96x^55+306x^56+658x^57+1092x^58+1446x^59+1642x^60+2808x^61+3168x^62+2284x^63+2928x^64+1776x^65+908x^66+312x^67+48x^68+86x^69+54x^70+54x^71+8x^72+6x^74+2x^81

The gray image is a linear code over GF(3) with n=279, k=9 and d=165.
This code was found by Heurico 1.16 in 0.48 seconds.