The generator matrix

 1  0  0  0  1  1  1  1  1
 0  1  0  0 2X^2+2X 2X^2+1 2X^2+X 2X^2+X+1 X+2
 0  0  1  0 2X^2+2X+1 2X^2+1 2X^2+X+1 2X^2+2X 2X+2
 0  0  0  1 2X^2+2X+2 2X^2+X 2X^2+2X 2X^2+2X+1 X+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+1812x^12+120x^13+8820x^14+10378x^15+75888x^16+34344x^17+199562x^18+151776x^19+34452x^20+13980x^21+150x^22+144x^23+14x^24

The gray image is a linear code over GF(3) with n=81, k=12 and d=36.
This code was found by Heurico 1.16 in 29.6 seconds.