The generator matrix

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

generates a code of length 6 over Z27 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+78x^12+2x^18

The gray image is a code over GF(3) with n=54, k=4 and d=36.
This code was found by Heurico 1.16 in 8.7e-005 seconds.