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
 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 18 18 18 18  0  9  9  0  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  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 18 18  9  0 18  9 18 18 18 18 18  0  9 18 18 18 18 18 18 18 18  9  0 18  0  9  0  9 18  0  9 18  0  0  0
 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  9  9 18 18  9  9 18  0  9 18 18  0  9  0  0 18  0  0  0 18  0  9 18 18 18  0 18  9  9  9  9  0  0  0
 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  9 18  0 18  0 18  9  0  0  0  9 18  0  0 18  9 18  0  9  0 18  9  9  9  9 18 18 18  0  0  0  0  0  0

generates a code of length 84 over Z27 who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+80x^162+1944x^168+160x^171+2x^252

The gray image is a code over GF(3) with n=756, k=7 and d=486.
This code was found by Heurico 1.16 in 0.293 seconds.