The generator matrix

 1  0  1  1  1  1  1  1 21 24  1  1  1  1  0  1  1 24  1  1  1  1  1  1 21  1  1  1 24  1 21  1  0  1  6  1  1  1  1 18  1  1 18  1  1  3  9 12  1  1 18  1  1  1  1 15  6  1  1  1  3  1  1  1  1  1  1  9
 0  1  1 26 21 24 20 23  1  1 16  4 18 17  1  1  3  1 23 25 22 24 26 20  1 21 14  0  1 15  1 16  1 19  1 14 21 19 21  1 26 13  1  5 15  1  1  1 18 15  1 14 26 17 19  1  1 19  1 25 18 26 12  1  2  2 26  3
 0  0 24  0  0  9 18  0  9  9 15 24 21 12  6  3 21 24 15 21 21  6  6  6  6 15 12  6  6  3 15  9 15 18 18 12  6  9  9 21  9 15 21 18  9 12  9 15 21 12 18  6  6 18 24 12  6 21  0  6 12 24 12 18  9  3  6 12
 0  0  0  9  0  0  0 18  9 18 18  9 18  0  0  0  9  9  9 18  9  0 18  0  9 18 18  9  0  9 18  0 18 18  9  9  0  9  9 18  0  0  0  9  9  0  9  9  0 18 18  0 18  0  0  9 18  9  9  9  0  9 18  0  9  9  0  9
 0  0  0  0 18  9  9 18  9 18  0  0 18  0  9  0  9 18  0  9 18  9  9 18  9 18  0 18 18  0 18  0  9 18 18  0  0  9 18  0  0 18  9 18  0 18  0  0 18  9  9  0 18 18  9  0  0 18 18  9  9  0 18 18  0  9 18 18

generates a code of length 68 over Z27 who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+718x^126+180x^127+486x^128+2596x^129+1188x^130+1692x^131+5658x^132+2574x^133+3528x^134+8368x^135+4734x^136+4014x^137+9448x^138+3402x^139+2844x^140+4506x^141+1044x^142+522x^143+896x^144+36x^146+364x^147+144x^150+88x^153+12x^156+6x^159

The gray image is a code over GF(3) with n=612, k=10 and d=378.
This code was found by Heurico 1.16 in 24.4 seconds.