The generator matrix

 1  0  1  1  1  1  1  3  1  1 24  1  1  3  1  1 21  1  1  1  1  1  1 21  1 21  1  1  1  1  1  1  1  1  0  1 15  1 18  6  1  1  1  1  0  1  1  1  1  1  1 24 18  1  3 12  1 15  1  1  1  1
 0  1  1 26 18 25 26  1  4 26  1 21 16  1 14 15  1 20  1 12 21 23 22  1 20  1 12 10  8 12 22 18 25 17  1  4  1 16  1  1  0  3 25 14  1  6  4 10  1 26  1  1  1 14  1  1 16  1 21 25 17  0
 0  0 24  0 18  0  0  9 18 18  0  9  9 12 24 12 24  3  3  6  6 12  6 15 24  3 21  3 15 12  6 24  3  6  3 15  9 24  6 12 12 24 21  3 15  0  3  6  6  6 12  3 24  9 12  9 12 24 15 21 12  0
 0  0  0  3 21 12  9  3 24  6 15  6  0 15  3  9 18  9 18  9 15 21 21 15 24  3 15 21  9 12  0 15  6 12  0 15 18  0 15  3  3 12  6 24  3  6 15  6  3  9  0  0 12 12  3 24  3 12 21  3 15  6

generates a code of length 62 over Z27 who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+136x^114+444x^115+606x^116+1498x^117+1830x^118+2136x^119+3946x^120+3744x^121+3990x^122+7240x^123+6450x^124+5460x^125+7916x^126+4944x^127+3234x^128+2688x^129+1158x^130+450x^131+472x^132+144x^133+72x^134+124x^135+174x^136+66x^137+24x^138+48x^139+24x^140+18x^142+10x^144+2x^147

The gray image is a code over GF(3) with n=558, k=10 and d=342.
This code was found by Heurico 1.16 in 9.03 seconds.