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  3  3  3  3  3  3  3  3  1  1  1  1  1  1  1  1  1  3  3  3  3  3  1  9  9  9  9  0  3  9  1  9  0  1  3  0  3  3  3
 0  9  0  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  9  9  9  0 18 18 18  0  0  9  9  0  9 18 18 18  0  9  9  9  0  0  9  9  9 18  9  0 18  0 18  9  0  0  9  9  9  9
 0  0  9 18 18  9  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0  0  9 18  9 18  9  0 18  0  9 18  0  9 18  9 18  0  0  9 18  9 18  9  0 18  0 18  9  0  0  9  0  9  9 18  0 18  0 18 18  9  0

generates a code of length 84 over Z27 who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+228x^168+4x^171+4x^180+6x^186

The gray image is a code over GF(3) with n=756, k=5 and d=504.
This code was found by Heurico 1.16 in 0.789 seconds.