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

generates a code of length 68 over Z27 who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+312x^124+792x^125+3194x^126+5586x^127+8916x^128+12690x^129+16692x^130+22830x^131+28090x^132+34734x^133+43032x^134+50008x^135+55044x^136+54966x^137+51238x^138+44514x^139+36498x^140+25706x^141+17172x^142+9822x^143+5574x^144+2262x^145+930x^146+494x^147+60x^148+72x^149+114x^150+18x^151+12x^152+38x^153+18x^154+6x^155+6x^157

The gray image is a code over GF(3) with n=612, k=12 and d=372.
This code was found by Heurico 1.16 in 542 seconds.