The generator matrix

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

generates a code of length 68 over Z27 who´s minimum homogenous weight is 131.

Homogenous weight enumerator: w(x)=1x^0+456x^131+784x^132+432x^133+822x^134+920x^135+366x^136+708x^137+604x^138+246x^139+378x^140+456x^141+84x^142+216x^143+52x^144+6x^145+6x^146+14x^150+2x^156+6x^158+2x^162

The gray image is a code over GF(3) with n=612, k=8 and d=393.
This code was found by Heurico 1.16 in 1.59 seconds.