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

generates a code of length 84 over Z27 who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+336x^161+114x^162+846x^164+342x^165+972x^167+216x^168+2916x^169+324x^170+18x^171+144x^173+36x^174+126x^179+144x^182+24x^188+2x^243

The gray image is a code over GF(3) with n=756, k=8 and d=483.
This code was found by Heurico 1.16 in 0.69 seconds.