The generator matrix

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

generates a code of length 80 over Z27 who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+1140x^148+1704x^149+4222x^150+7494x^151+9750x^152+13810x^153+18762x^154+23304x^155+29056x^156+36444x^157+39246x^158+45770x^159+51090x^160+48120x^161+47416x^162+44694x^163+33990x^164+26934x^165+20934x^166+12522x^167+7468x^168+4152x^169+1812x^170+868x^171+354x^172+108x^173+92x^174+54x^175+24x^176+32x^177+30x^178+6x^179+14x^180+18x^181+6x^183

The gray image is a code over GF(3) with n=720, k=12 and d=444.
This code was found by Heurico 1.16 in 689 seconds.