The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+330x^40+336x^41+512x^42+1446x^43+2418x^44+1794x^45+4038x^46+4608x^47+1776x^48+1830x^49+330x^50+26x^51+120x^52+84x^53+14x^54+12x^55+6x^57+2x^60

The gray image is a linear code over GF(3) with n=207, k=9 and d=120.
This code was found by Heurico 1.16 in 11.6 seconds.