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

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

Homogenous weight enumerator: w(x)=1x^0+90x^123+222x^126+1458x^128+324x^129+54x^132+18x^135+18x^141+2x^189

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 0.191 seconds.