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

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

Homogenous weight enumerator: w(x)=1x^0+30x^168+52x^171+324x^172+1026x^174+648x^175+94x^177+10x^180+2x^258

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 0.4 seconds.