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

generates a code of length 61 over Z27 who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+6x^109+42x^110+194x^111+150x^112+132x^113+388x^114+330x^115+396x^116+524x^117+1470x^118+1134x^119+578x^120+3552x^121+2232x^122+750x^123+3624x^124+1506x^125+598x^126+894x^127+228x^128+378x^129+132x^130+120x^131+136x^132+42x^133+42x^134+20x^135+6x^136+18x^138+18x^141+10x^144+18x^147+4x^150+8x^153+2x^156

The gray image is a code over GF(3) with n=549, k=9 and d=327.
This code was found by Heurico 1.16 in 41.1 seconds.