The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^9+192x^12+162x^14+786x^15+1944x^16+648x^17+10236x^18+3888x^19+648x^20+1050x^21+78x^24+20x^27

The gray image is a linear code over GF(3) with n=81, k=9 and d=27.
This code was found by Heurico 1.16 in 0.0587 seconds.