The generator matrix

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

generates a code of length 65 over Z27 who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+1038x^124+1086x^125+1524x^126+2364x^127+1860x^128+1320x^129+2112x^130+1734x^131+1216x^132+1890x^133+1014x^134+656x^135+1014x^136+444x^137+218x^138+156x^139+6x^140+2x^141+6x^142+6x^143+6x^145+4x^147+6x^149

The gray image is a code over GF(3) with n=585, k=9 and d=372.
This code was found by Heurico 1.16 in 1.22 seconds.