The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+444x^36+540x^39+486x^40+4662x^42+1944x^43+8160x^45+1944x^46+1188x^48+144x^51+170x^54

The gray image is a linear code over GF(3) with n=198, k=9 and d=108.
This code was found by Heurico 1.16 in 90.1 seconds.