The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+132x^43+36x^44+66x^46+4x^48+4x^51

The gray image is a linear code over GF(3) with n=198, k=5 and d=129.
This code was found by Heurico 1.16 in 0.00183 seconds.