The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+28x^39+82x^42+486x^44+88x^45+26x^48+8x^51+10x^54

The gray image is a linear code over GF(3) with n=198, k=6 and d=117.
This code was found by Heurico 1.16 in 0.00322 seconds.