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

generates a code of length 65 over Z27 who´s minimum homogenous weight is 130.

Homogenous weight enumerator: w(x)=1x^0+54x^130+14x^132+2x^135+8x^138+2x^144

The gray image is a code over GF(3) with n=585, k=4 and d=390.
This code was found by Heurico 1.16 in 0.0868 seconds.