The generator matrix

 1  1  1  1  1  1  0  1  1
 0  X  0  0 2X^2  X X^2 2X^2+X  X
 0  0  X  0 2X^2+X 2X  X 2X 2X^2+X
 0  0  0  X 2X^2+2X X^2+X 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+156x^12+120x^13+396x^14+442x^15+2016x^16+648x^17+10076x^18+4032x^19+756x^20+732x^21+150x^22+144x^23+14x^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 0.107 seconds.