The generator matrix

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

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+480x^18+1296x^21+2592x^24+2168x^27+24x^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 0.0644 seconds.