The generator matrix

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

generates a code of length 31 over Z27 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+60x^62+2x^63+12x^65+6x^66

The gray image is a code over GF(3) with n=279, k=4 and d=186.
This code was found by Heurico 1.16 in 0.00562 seconds.