The generator matrix

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

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+654x^12+144x^13+3096x^14+3432x^15+23220x^16+11448x^17+72096x^18+46440x^19+11556x^20+4728x^21+180x^22+144x^23+6x^24+2x^27

The gray image is a linear code over GF(3) with n=81, k=11 and d=36.
This code was found by Heurico 1.16 in 3.6 seconds.