The generator matrix

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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+404x^147+642x^148+1860x^149+3058x^150+2670x^151+3630x^152+6026x^153+3744x^154+4572x^155+6744x^156+4170x^157+4452x^158+5302x^159+3144x^160+2958x^161+2614x^162+930x^163+876x^164+738x^165+216x^166+96x^167+82x^168+18x^169+18x^170+26x^171+6x^172+6x^173+34x^174+12x^175

The gray image is a code over GF(3) with n=702, k=10 and d=441.
This code was found by Heurico 1.16 in 9.64 seconds.