The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+638x^114+1158x^115+2904x^116+4102x^117+5028x^118+7608x^119+9464x^120+12612x^121+16134x^122+16766x^123+16962x^124+20946x^125+17366x^126+14958x^127+12624x^128+7960x^129+4530x^130+2646x^131+1526x^132+522x^133+228x^134+176x^135+60x^136+54x^137+60x^138+48x^139+30x^140+12x^141+6x^142+6x^143+6x^144+6x^145

The gray image is a code over GF(3) with n=558, k=11 and d=342.
This code was found by Heurico 1.16 in 61 seconds.