The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  0  1  0  1  1  1  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X X^2 2X 2X^2+X 2X^2+X  0 X^2 2X X^2+X 2X^2+2X  0  X X^2 2X^2+2X 2X^2 2X^2+X  X  0  X  X  X 2X^2+X X^2+2X
 0  0  X 2X  0 X^2+2X X^2+X  X X^2+2X 2X^2 X^2+2X 2X^2+2X  0 X^2+X 2X^2+2X X^2 2X 2X^2+X 2X X^2+X  X  0 2X X^2 X^2 X^2+X 2X  0 X^2+X 2X  X
 0  0  0 X^2  0  0 2X^2  0  0 X^2 2X^2 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0 2X^2  0 2X^2  0 X^2 2X^2  0 2X^2 X^2
 0  0  0  0 X^2 2X^2  0 X^2 2X^2  0 2X^2 2X^2  0  0  0 2X^2  0 X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 2X^2  0 2X^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+486x^54+1122x^57+810x^58+2334x^60+3240x^61+2916x^62+3534x^63+3240x^64+1266x^66+600x^69+120x^72+6x^75+8x^81

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 27 seconds.