The generator matrix

 1  1  1  1  1  1  1  1  1
 0  3  0  9 24 21  3 15 24
 0  0  3 15  9  6  3 21 15

generates a code of length 9 over Z27 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+216x^15+1752x^18+216x^21+2x^27

The gray image is a code over GF(3) with n=81, k=7 and d=45.
This code was found by Heurico 1.16 in 0.00226 seconds.