The generator matrix

 1  0  1  1  1  1  1  0  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X^2+2X+1
 0  0 2X^2  0  0 X^2 2X^2 X^2 2X^2
 0  0  0 X^2  0 2X^2 2X^2  0 2X^2
 0  0  0  0 2X^2 2X^2 X^2 X^2 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+54x^12+486x^14+180x^15+2430x^16+1944x^17+7530x^18+4860x^19+1944x^20+216x^21+36x^24+2x^27

The gray image is a linear code over GF(3) with n=81, k=9 and d=36.
This code was found by Heurico 1.16 in 0.056 seconds.