The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+354x^130+324x^131+264x^132+900x^133+756x^134+200x^135+990x^136+810x^137+64x^138+762x^139+486x^140+164x^141+366x^142+54x^143+20x^144+18x^145+8x^147+12x^151+2x^153+4x^159+2x^171

The gray image is a code over GF(3) with n=612, k=8 and d=390.
This code was found by Heurico 1.16 in 7.56 seconds.