The generator matrix

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

generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+162x^16+36x^17+182x^18+324x^19+18x^20+6x^21

The gray image is a linear code over GF(3) with n=81, k=6 and d=48.
This code was found by Heurico 1.16 in 0.00032 seconds.