The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+540x^39+576x^40+1734x^41+2334x^42+2130x^43+3834x^44+3768x^45+2124x^46+1710x^47+864x^48+18x^49+12x^50+24x^51+12x^52+2x^54

The gray image is a linear code over GF(3) with n=198, k=9 and d=117.
This code was found by Heurico 1.16 in 0.235 seconds.