The generator matrix

 1  1  1  1  1  1  1  1  1  3  3  3
 0  9  0  0  0  0  0  9  9  9  9  9
 0  0  9  0  0  0  9 18 18  9  9  0
 0  0  0  9  0  0 18 18  9  0  9 18
 0  0  0  0  9  0 18  9 18  9  0 18
 0  0  0  0  0  9  9  0  9  9 18 18

generates a code of length 12 over Z27 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+318x^18+324x^21+5022x^24+872x^27+24x^36

The gray image is a code over GF(3) with n=108, k=8 and d=54.
This code was found by Heurico 1.16 in 0.0273 seconds.