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

generates a code of length 64 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+54x^123+48x^124+160x^126+60x^127+1620x^128+104x^129+18x^130+42x^132+24x^133+34x^135+12x^136+8x^138+2x^192

The gray image is a code over GF(3) with n=576, k=7 and d=369.
This code was found by Heurico 1.16 in 0.14 seconds.