The generator matrix

 1  0  0  1  1  1  1  1  9  1  1  1 15  1  1  1  1  3 24  1  1  1 15 18  1  1 12  1 12  1  1  1  1 24  1  1  1  1 12  1  9  1 15  1 21  1  1  1  0  1  1  1  1  1 24  1  1  1  1  1 18  0  1  1  1 21  1  1
 0  1  0 18  1 19 23 21  1  4  5 26  1  9 22  7 20  1  1 16 11 24 21  1  8 14  1  6 12 11  7 20  4  1 16  3 10 23  0  5  1  3  1  3  1 11 16 24  1 22  1  0  9 14 15 13 10  2 24 15  6  1 26 17 19  6  5 25
 0  0  1 16 25 18 17  8 22  5 22  6 20 21  7  9 23  0 13 14 10 26  1 12 11  3 14 25  1 12  6 16  1 14 17  1 15 10  1 24  2 21 19  0 26 13  3 23 10  4  4 10 15  9  1  6 16  8  3 22  1  7 22  7 12  1  5 15

generates a code of length 68 over Z27 who´s minimum homogenous weight is 130.

Homogenous weight enumerator: w(x)=1x^0+918x^130+1320x^131+1528x^132+2376x^133+1728x^134+1654x^135+2118x^136+1398x^137+1138x^138+1776x^139+1128x^140+666x^141+810x^142+558x^143+266x^144+252x^145+24x^146+8x^147+6x^148+2x^150+6x^154+2x^162

The gray image is a code over GF(3) with n=612, k=9 and d=390.
This code was found by Heurico 1.16 in 1.03 seconds.