The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  1  1  1  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X^2+1 2X+2  1 X^2 X^2+2X+1 X^2+2 X^2+X X^2+X+1 X^2+X+2 X^2+2X X^2+1 X^2+2X+2 2X^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+288x^43+108x^44+122x^45+144x^46+4x^48+2x^57

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 0.00172 seconds.