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

generates a code of length 62 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+14x^123+198x^124+8x^126+18x^127+2x^132+2x^150

The gray image is a code over GF(3) with n=558, k=5 and d=369.
This code was found by Heurico 1.16 in 0.0722 seconds.