The generator matrix

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

generates a code of length 31 over Z27 who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+108x^59+198x^60+348x^63+18x^66+54x^68+2x^81

The gray image is a code over GF(3) with n=279, k=6 and d=177.
This code was found by Heurico 1.16 in 0.405 seconds.