The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1
 0  9  0  0  0  0  0  0  9  9  9  0
 0  0  9  0  0  0  0  9 18  9 18  0
 0  0  0  9  0  0  0 18 18  0  9  0
 0  0  0  0  9  0  0 18 18  9  0  0
 0  0  0  0  0  9  0 18 18 18  0  9
 0  0  0  0  0  0  9 18  9  9 18  0

generates a code of length 12 over Z27 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+66x^12+168x^15+138x^18+444x^21+18006x^24+404x^27+300x^30+132x^33+24x^36

The gray image is a code over GF(3) with n=108, k=9 and d=36.
This code was found by Heurico 1.16 in 0.117 seconds.