The generator matrix

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

generates a code of length 31 over Z27 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+60x^61+144x^62+30x^64+2x^66+4x^69+2x^75

The gray image is a code over GF(3) with n=279, k=5 and d=183.
This code was found by Heurico 1.16 in 0.0056 seconds.