The generator matrix

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

generates a code of length 77 over Z27 who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+654x^142+1332x^143+4352x^144+7254x^145+9528x^146+13904x^147+19026x^148+21192x^149+28948x^150+36906x^151+38244x^152+49268x^153+51534x^154+47778x^155+51212x^156+45108x^157+32106x^158+27154x^159+20352x^160+11550x^161+7360x^162+3960x^163+1446x^164+680x^165+288x^166+78x^167+76x^168+30x^169+24x^170+12x^171+36x^172+12x^174+18x^175+12x^176+6x^179

The gray image is a code over GF(3) with n=693, k=12 and d=426.
This code was found by Heurico 1.16 in 660 seconds.