The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+162x^36+324x^38+216x^39+18x^42+6x^45+2x^54

The gray image is a linear code over GF(3) with n=171, k=6 and d=108.
This code was found by Heurico 1.16 in 0.0164 seconds.