The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+366x^38+270x^39+594x^40+1866x^41+1472x^42+2376x^43+5106x^44+2454x^45+2376x^46+2172x^47+360x^48+204x^50+56x^51+6x^53+2x^54+2x^60

The gray image is a linear code over GF(3) with n=198, k=9 and d=114.
This code was found by Heurico 1.16 in 0.334 seconds.