The generator matrix

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

generates a code of length 8 over Z27 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+14x^15+54x^16+10x^18+2x^21

The gray image is a code over GF(3) with n=72, k=4 and d=45.
This code was found by Heurico 1.16 in 0.000134 seconds.