The generator matrix

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

generates a code of length 60 over Z27 who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+746x^114+858x^115+2100x^116+1906x^117+1794x^118+2250x^119+1882x^120+1350x^121+1938x^122+1420x^123+984x^124+852x^125+796x^126+348x^127+306x^128+118x^129+6x^131+12x^132+12x^133+4x^138

The gray image is a code over GF(3) with n=540, k=9 and d=342.
This code was found by Heurico 1.16 in 0.79 seconds.