The generator matrix

 1  0  0  1  1  1  1  0  1  1  1  1 18  1  1  1  1  1 24  1  1 18  1  1 12 21  1  1 12 15  1  1  1  1  9  9  1  1  6  1  1  1  1  1  6  1 15  1  1  1  3  1  6  1 15 15  1  1  1  1  1  1  1  1  1
 0  1  0  0  9 16 17  1 16 17 25  8  1 25 15  8 14 24  1  2 19  1 13 15  0  1  1 21  1  1 14  5  5  3 12  1  7 18  1 23  8 10 26 16  1 12 18  0 17 15 24 10  9  5  1  1 21 10  6  5 13 16 10 14 13
 0  0  1  7 17  8 20  5 18 21  1 25 16 25 11  9  7 13 10 20 17 20  9 12  1  3  1 22 16 23  3  8  1 21  1 12  5  3 16  0 22  0 23 11  9 16  1  4 19 17  1 13  1  4 13  1 23 17  8 20 11 26  3  1 26
 0  0  0  9 18 18 18 18  0  0  9  9  9  0  9 18 18 18 18  0  0  0  9 18 18  9 18  0  0  9  0  9  0 18  9 18  9  9  9  9  0  0 18  9  0  0 18 18  9  0  0 18  9  0 18  9  0  9 18 18  0  0  9 18 18

generates a code of length 65 over Z27 who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+948x^122+788x^123+2214x^124+4182x^125+3508x^126+4104x^127+6708x^128+3898x^129+4896x^130+7386x^131+4568x^132+4320x^133+5220x^134+2058x^135+1674x^136+1554x^137+436x^138+288x^139+180x^140+38x^141+42x^143+4x^144+18x^146+4x^147+6x^150+6x^152

The gray image is a code over GF(3) with n=585, k=10 and d=366.
This code was found by Heurico 1.16 in 47.6 seconds.