The generator matrix

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

generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+306x^12+1458x^14+1692x^15+7290x^16+5832x^17+19788x^18+14580x^19+5832x^20+2232x^21+36x^24+2x^27

The gray image is a linear code over GF(3) with n=81, k=10 and d=36.
This code was found by Heurico 1.16 in 8.94 seconds.