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  1  3  1  1  1  1  1  3  3  1  1  1  3  3  3  1  3  1  3  3  9  9  0  3  3  3  3  9  3  1
 0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  9  0 18  9 18  0  9 18  9 18  0  9 18  9 18  0  0  0  9  9 18  9 18  9  0  0  9 18  0  0 18

generates a code of length 61 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+72x^123+2x^126+6x^129

The gray image is a code over GF(3) with n=549, k=4 and d=369.
This code was found by Heurico 1.16 in 0.0681 seconds.