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

generates a code of length 65 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+364x^123+18x^124+812x^126+108x^127+1826x^129+1188x^130+1572x^132+144x^133+200x^135+148x^138+80x^141+74x^144+24x^147+2x^180

The gray image is a code over GF(3) with n=585, k=8 and d=369.
This code was found by Heurico 1.16 in 0.37 seconds.