The generator matrix

 1  1  1
 0  3 24

generates a code of length 3 over Z27 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+186x^6+36x^7+2x^9

The gray image is a code over GF(3) with n=27, k=5 and d=12.
This code was found by Heurico 1.16 in 4.89e-005 seconds.