The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1  1  1  3  3  1  3  3  3  1  1  1  3  1  3  3
 0  3  0  0 24 21  3 15 24 21 18  0 21 15  9 24 15 21  3 15 12 18  3 18 24  9 15 24  0  6 15 12  9 18 24  3 21 12 15 21  0  9 21  9 15 15  3  0 21  0 18 18 24 24  3 24  6 15 18  0 15 24 12  3 21 21 18 18  9  9 18  0  6 24 24  0 21  9 15 24 24  9  0  3 15 24
 0  0  3 24  0 15  3 21  6  6 21  0  3 21 15  9 24  9  3 12  6  3  9 24  9 18 24 21 18  9 15  6 21  6  3 21  6 12  6 18 21  6 24 24  9 12  9 12 12 21  0 24 18 24 21  3  0 21 15 18  6  9  9 18  9 24  0  0 18  3  3 24 15  6 18 24  0  3 12 21  9 18 21  9 21 18
 0  0  0  9  0  0  0 18  0  9 18  9 18  9 18  0  9 18  9  0 18  9  9  0  0 18  0 18  9 18 18 18  0  0  9  9 18 18  0  9 18 18  0  9  9  9 18  0 18  9  0 18 18  9  9  0  9 18  9 18  9 18  0  0  9  9 18  0  9  9 18 18  0  0  0 18  9  0 18  9  9 18  9 18  9 18
 0  0  0  0  9 18  9  0 18  0 18  9  0  0  0  0  0 18 18  9  9 18  9  0 18  0  9 18 18  0 18 18 18 18  9  0  0  9  0 18  9 18  0 18 18 18  9  9 18  9  9  9 18  9  9 18  9  9  9  9 18  9  9 18  0  9  9 18  0  9  0 18 18  0 18  0 18 18  0 18  9 18  9  0 18 18

generates a code of length 86 over Z27 who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+246x^161+248x^162+18x^163+672x^164+408x^165+198x^166+1008x^167+1272x^168+648x^169+1602x^170+3348x^171+1062x^172+1734x^173+3312x^174+882x^175+1074x^176+430x^177+108x^178+348x^179+178x^180+234x^182+156x^183+210x^185+80x^186+108x^188+14x^189+42x^191+28x^192+12x^194+2x^228

The gray image is a code over GF(3) with n=774, k=9 and d=483.
This code was found by Heurico 1.16 in 3.2 seconds.