The generator matrix

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

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+24x^18+54x^22+36x^24+108x^25+2x^27+18x^33

The gray image is a linear code over GF(3) with n=36, k=5 and d=18.
This code was found by Heurico 1.16 in 0.000533 seconds.