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

generates a code of length 31 over Z27 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+258x^58+242x^60+510x^61+324x^62+268x^63+438x^64+48x^66+48x^67+4x^69+12x^70+2x^72+30x^73+2x^81

The gray image is a code over GF(3) with n=279, k=7 and d=174.
This code was found by Heurico 1.16 in 51.3 seconds.