The generator matrix

 1  1  1  1  1  1
 0  3 24  9 21  6

generates a code of length 6 over Z27 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+36x^11+186x^12+18x^14+2x^18

The gray image is a code over GF(3) with n=54, k=5 and d=33.
This code was found by Heurico 1.16 in 0.000122 seconds.