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

generates a code of length 87 over Z27 who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+30x^168+40x^171+2034x^174+60x^177+20x^180+2x^261

The gray image is a code over GF(3) with n=783, k=7 and d=504.
This code was found by Heurico 1.16 in 0.331 seconds.