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

generates a code of length 63 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+68x^123+180x^124+108x^126+288x^127+48x^129+18x^130+16x^132+2x^171

The gray image is a code over GF(3) with n=567, k=6 and d=369.
This code was found by Heurico 1.16 in 0.106 seconds.