The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^6+16x^9+666x^12+24x^15+10x^18

The gray image is a code over GF(3) with n=54, k=6 and d=18.
This code was found by Heurico 1.16 in 0.000159 seconds.