The generator matrix

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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+450x^145+984x^146+2138x^147+3468x^148+4590x^149+7028x^150+8160x^151+9738x^152+12024x^153+13608x^154+14850x^155+17178x^156+17166x^157+14862x^158+15320x^159+11604x^160+8766x^161+6418x^162+4092x^163+2244x^164+1198x^165+534x^166+240x^167+104x^168+120x^169+66x^170+46x^171+48x^172+12x^173+18x^174+36x^175+18x^176+6x^177+6x^178+6x^179

The gray image is a code over GF(3) with n=702, k=11 and d=435.
This code was found by Heurico 1.16 in 78.8 seconds.