The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+438x^18+1422x^21+2538x^24+2018x^27+144x^30

The gray image is a linear code over GF(3) with n=36, k=8 and d=18.
This code was found by Heurico 1.16 in 0.078 seconds.