The generator matrix

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

generates a code of length 60 over Z27 who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+786x^109+1800x^110+4534x^111+7398x^112+10506x^113+16850x^114+21552x^115+27804x^116+36472x^117+44652x^118+52746x^119+58206x^120+57636x^121+53706x^122+47288x^123+36342x^124+24054x^125+15236x^126+7920x^127+3210x^128+1844x^129+540x^130+78x^131+74x^132+66x^133+54x^134+38x^135+12x^136+24x^137+6x^138+6x^140

The gray image is a code over GF(3) with n=540, k=12 and d=327.
This code was found by Heurico 1.16 in 473 seconds.