The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+60x^42+36x^43+540x^44+56x^45+18x^46+16x^48+2x^66

The gray image is a linear code over GF(3) with n=198, k=6 and d=126.
This code was found by Heurico 1.16 in 0.00343 seconds.