The generator matrix

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

generates a code of length 79 over Z27 who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+936x^146+1856x^147+4134x^148+6810x^149+10500x^150+13650x^151+19134x^152+22730x^153+28122x^154+36924x^155+39544x^156+44538x^157+51486x^158+50872x^159+47568x^160+43566x^161+35064x^162+26784x^163+20712x^164+12124x^165+6882x^166+4236x^167+1796x^168+756x^169+318x^170+138x^171+48x^172+48x^173+68x^174+48x^175+18x^176+18x^177+6x^180+6x^182

The gray image is a code over GF(3) with n=711, k=12 and d=438.
This code was found by Heurico 1.16 in 681 seconds.