The generator matrix

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

generates a code of length 62 over Z27 who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+1158x^113+1910x^114+4404x^115+8016x^116+10918x^117+16830x^118+22800x^119+26670x^120+36690x^121+47148x^122+46988x^123+57018x^124+61620x^125+50152x^126+47142x^127+37008x^128+23634x^129+15456x^130+9438x^131+3536x^132+1716x^133+774x^134+174x^135+48x^136+90x^137+24x^138+18x^139+18x^140+18x^141+6x^142+6x^143+6x^145+6x^146

The gray image is a code over GF(3) with n=558, k=12 and d=339.
This code was found by Heurico 1.16 in 491 seconds.