The generator matrix

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

generates a code of length 77 over Z27 who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+234x^143+294x^144+486x^145+1518x^146+1160x^147+1944x^148+3342x^149+2000x^150+4248x^151+5898x^152+3852x^153+6444x^154+7092x^155+4262x^156+5076x^157+4704x^158+1724x^159+2124x^160+1326x^161+302x^162+90x^163+402x^164+146x^165+144x^167+62x^168+84x^170+18x^171+42x^173+8x^174+12x^177+6x^180+2x^183+2x^192

The gray image is a code over GF(3) with n=693, k=10 and d=429.
This code was found by Heurico 1.16 in 11.7 seconds.