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

generates a code of length 86 over Z27 who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+144x^169+24x^170+72x^171+324x^172+24x^173+48x^174+6x^176+72x^178+8x^180+6x^186

The gray image is a code over GF(3) with n=774, k=6 and d=507.
This code was found by Heurico 1.16 in 0.349 seconds.