The generator matrix

 1  1  1  1  1  1  1  1
 0  3 24  9 21  6 18 12

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

Homogenous weight enumerator: w(x)=1x^0+16x^15+216x^16+8x^18+2x^24

The gray image is a code over GF(3) with n=72, k=5 and d=45.
This code was found by Heurico 1.16 in 0.000189 seconds.