The generator matrix

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

generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+48x^15+486x^16+636x^18+972x^19+36x^21+6x^24+2x^27

The gray image is a linear code over GF(3) with n=81, k=7 and d=45.
This code was found by Heurico 1.16 in 0.103 seconds.