The generator matrix

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

generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+156x^12+120x^13+396x^14+442x^15+558x^16+648x^17+1328x^18+1116x^19+756x^20+732x^21+150x^22+144x^23+14x^24

The gray image is a linear code over GF(3) with n=27, k=8 and d=12.
This code was found by Heurico 1.16 in 0.031 seconds.