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

generates a code of length 68 over Z27 who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+182x^129+402x^130+216x^132+774x^133+648x^134+332x^135+1176x^136+1296x^137+296x^138+798x^139+44x^141+96x^142+18x^144+90x^145+62x^147+24x^148+62x^150+30x^151+12x^154+2x^186

The gray image is a code over GF(3) with n=612, k=8 and d=387.
This code was found by Heurico 1.16 in 1.09 seconds.