The generator matrix

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

generates a code of length 6 over Z27 who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+24x^9+192x^12+24x^15+2x^18

The gray image is a code over GF(3) with n=54, k=5 and d=27.
This code was found by Heurico 1.16 in 0.000106 seconds.