The generator matrix

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

generates a code of length 77 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+774x^144+234x^145+756x^146+2400x^147+1944x^148+2448x^149+4158x^150+3582x^151+4194x^152+5466x^153+5382x^154+5328x^155+6168x^156+4698x^157+4032x^158+3426x^159+1494x^160+720x^161+902x^162+162x^163+18x^164+408x^165+186x^168+120x^171+42x^174+6x^177

The gray image is a code over GF(3) with n=693, k=10 and d=432.
This code was found by Heurico 1.16 in 14.2 seconds.