The generator matrix

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

generates a code of length 31 over Z27 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+342x^60+294x^63+72x^66+18x^69+2x^81

The gray image is a code over GF(3) with n=279, k=6 and d=180.
This code was found by Heurico 1.16 in 6.61 seconds.