The generator matrix

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

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+62x^12+504x^14+236x^15+2268x^16+1620x^17+8342x^18+4536x^19+1728x^20+334x^21+36x^23+16x^24

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 0.0664 seconds.