The generator matrix

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

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+422x^54+54x^55+180x^56+1374x^57+522x^58+756x^59+2778x^60+1836x^61+2322x^62+4158x^63+1836x^64+1116x^65+1380x^66+126x^67+678x^69+144x^72

The gray image is a linear code over GF(3) with n=279, k=9 and d=162.
This code was found by Heurico 1.16 in 0.983 seconds.