The generator matrix

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

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+498x^18+1206x^21+2808x^24+1898x^27+144x^30+6x^36

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 2.04 seconds.