The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1
 0 X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 X^2  0 2X^2 X^2 2X^2  0 X^2 2X^2  0 X^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+12x^43+54x^44+4x^45+6x^46+2x^48+2x^60

The gray image is a linear code over GF(3) with n=198, k=4 and d=129.
This code was found by Heurico 1.16 in 0.00162 seconds.