The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^12+168x^15+138x^18+444x^21+4884x^24+404x^27+300x^30+132x^33+24x^36

The gray image is a linear code over GF(3) with n=36, k=8 and d=12.
This code was found by Heurico 1.16 in 0.0239 seconds.