The generator matrix

 1  0  1  1  1  1  1 21  1
 0  1 16 26 21  4 20  1 24

generates a code of length 9 over Z27 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+162x^16+36x^17+182x^18+324x^19+18x^20+6x^21

The gray image is a code over GF(3) with n=81, k=6 and d=48.
This code was found by Heurico 1.16 in 0.000314 seconds.