The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X
 0  X  0 X^2 2X 2X^2+X  X 2X^2+2X 2X X^2 2X^2+X 2X^2+2X 2X^2 X^2  X X^2+2X 2X^2+X 2X  0 2X^2+X 2X^2 2X^2+X
 0  0  X 2X^2+2X X^2 2X^2+2X  X 2X^2+X X^2+2X X^2 2X^2+X 2X  X 2X^2 X^2 2X^2+X 2X^2 X^2+X 2X  X 2X^2+2X 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+168x^40+338x^42+228x^43+648x^44+510x^45+162x^46+36x^48+48x^49+2x^51+42x^52+2x^54+2x^60

The gray image is a linear code over GF(3) with n=198, k=7 and d=120.
This code was found by Heurico 1.16 in 0.101 seconds.