The generator matrix

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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+932x^144+1296x^145+4422x^146+8208x^147+9180x^148+12678x^149+19972x^150+20262x^151+28926x^152+39754x^153+37326x^154+44778x^155+56214x^156+46794x^157+46590x^158+48250x^159+32166x^160+26514x^161+22428x^162+10476x^163+7362x^164+4074x^165+1302x^166+732x^167+508x^168+66x^169+12x^170+92x^171+36x^172+12x^173+12x^174+12x^176+30x^177+12x^178+6x^179+6x^181

The gray image is a code over GF(3) with n=702, k=12 and d=432.
This code was found by Heurico 1.16 in 671 seconds.