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

generates a code of length 68 over Z27 who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+138x^127+66x^129+318x^130+310x^132+276x^133+972x^134+830x^135+162x^136+1944x^137+856x^138+210x^139+84x^141+150x^142+20x^144+72x^145+12x^147+66x^148+60x^151+2x^153+6x^154+2x^159+2x^165+2x^189

The gray image is a code over GF(3) with n=612, k=8 and d=381.
This code was found by Heurico 1.16 in 0.838 seconds.