The generator matrix

 1  0  1  1  1  1  1  1  X
 0  1  1  2  0 2X+1 2X^2+1 2X^2+2X+1 2X^2+X
 0  0 2X  0 X^2  X X^2 X^2+2X 2X^2+X
 0  0  0  X 2X^2+2X 2X^2 2X^2 X^2+2X X^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+318x^12+120x^13+1368x^14+1414x^15+7848x^16+4536x^17+20768x^18+15696x^19+4644x^20+2028x^21+150x^22+144x^23+14x^24

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 0.529 seconds.