The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1
 0  3  0  0  0  0  0  0  3  3  3  0
 0  0  3  0  0  0  0  3  6  3  6  0
 0  0  0  3  0  0  0  6  6  0  3  0
 0  0  0  0  3  0  0  6  6  3  0  0
 0  0  0  0  0  3  0  6  6  6  0  3
 0  0  0  0  0  0  3  6  3  3  6  0

generates a code of length 12 over Z9 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 code over GF(3) with n=36, k=8 and d=12.
This code was found by Heurico 1.16 in 0.0332 seconds.