The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  0  1  1  1  3  3  9  3  3 18  1  1  1  1  1  1  1  1  1  3  3  3  3  3  3  3  0  9  3  3
 0  3 24  9 21  6 18 12 15  0 21 24  9 12  6 18  3 15  0 21 24  9 12  6 18  3 15  0 21 24  9 12  6 21 24  3 18  3 15 12  6  3  3 15  3  0  9 18 21 12  3 24  6 15  0  9 18 21 12 24  6  3  3  3 15

generates a code of length 65 over Z27 who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+36x^129+162x^130+30x^132+8x^135+6x^141

The gray image is a code over GF(3) with n=585, k=5 and d=387.
This code was found by Heurico 1.16 in 0.0866 seconds.