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

generates a code of length 88 over Z27 who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+36x^172+90x^173+28x^174+144x^175+1602x^176+48x^177+144x^178+90x^179+2x^180+2x^264

The gray image is a code over GF(3) with n=792, k=7 and d=516.
This code was found by Heurico 1.16 in 0.318 seconds.