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

generates a code of length 65 over Z27 who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+112x^126+144x^127+276x^128+294x^129+582x^130+336x^131+292x^132+48x^133+12x^134+16x^135+12x^136+24x^137+12x^138+24x^139+2x^186

The gray image is a code over GF(3) with n=585, k=7 and d=378.
This code was found by Heurico 1.16 in 0.114 seconds.