The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1
 0  1  1  2  0 2X+1  2  1  0  0  X  X
 0  0 2X  0  0 2X 2X  X  0  X 2X  X
 0  0  0  X  0 2X  0 2X 2X 2X 2X  X
 0  0  0  0  X 2X  X 2X  X  X  0 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+108x^18+162x^20+168x^21+648x^23+180x^24+648x^26+152x^27+120x^30

The gray image is a linear code over GF(3) with n=36, k=7 and d=18.
This code was found by Heurico 1.16 in 0.0101 seconds.