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  3  3  3  3  3  3  3  3  3  3  1  1  1  1  3  3  1  3  3  3  3  3  1
 0  9  0  0  0  0  9 18 18  0  0  9  9  9  9  9  9  9  0 18  0 18  0 18  0  9 18  9 18 18  0  0 18  9  0  9  9  9  9  0  0  0  9  0  9  0  9  9  9  9  9 18 18  9  9  0  0  9  9 18 18  0 18 18 18  9 18 18
 0  0  9  0  0  9 18  0 18  0  9  9 18 18  0  9  0  9  9  9  9  0  0 18 18  9  9 18  0 18  0  9  9  0 18 18  0  9  0 18 18 18  9 18 18  0 18 18  9  9  0  9 18  0  0  0  0 18  9  0  0 18 18  9  0 18  0  9
 0  0  0  9  0 18 18  9  0  9  9  0  0  9 18  9  9 18 18  0  0 18 18 18 18 18  9  9  0  9 18  9 18 18  9 18  9  0  0  0  9  0  9 18  0  0 18  9  0 18 18  0 18  9  0  0  9  9  0  0 18 18 18  0 18 18  0 18
 0  0  0  0  9 18 18 18 18 18  0 18  0  0 18 18  0  9  0  0 18 18  9 18  9 18  0 18  0  0 18 18  9  0  0  0 18  0  9  9 18 18  9  0  9  9 18  9  9 18  0  9  9  9  9 18  9  9  9  0  0 18  0 18 18  0 18  0

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

Homogenous weight enumerator: w(x)=1x^0+118x^129+192x^132+124x^135+1458x^136+124x^138+66x^141+50x^144+28x^147+2x^150+10x^153+8x^159+2x^162+2x^168+2x^171

The gray image is a code over GF(3) with n=612, k=7 and d=387.
This code was found by Heurico 1.16 in 0.15 seconds.