The generator matrix

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

generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+648x^14+216x^15+1944x^16+2592x^17+7584x^18+3888x^19+2592x^20+216x^21+2x^27

The gray image is a linear code over GF(3) with n=81, k=9 and d=42.
This code was found by Heurico 1.16 in 3.87 seconds.