The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+414x^40+702x^41+446x^42+1254x^43+1026x^44+726x^45+1152x^46+702x^47+36x^48+54x^49+2x^51+42x^52+2x^54+2x^60

The gray image is a linear code over GF(3) with n=198, k=8 and d=120.
This code was found by Heurico 1.16 in 14.9 seconds.