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

generates a code of length 83 over Z27 who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+80x^162+1944x^166+160x^168+2x^249

The gray image is a code over GF(3) with n=747, k=7 and d=486.
This code was found by Heurico 1.16 in 0.283 seconds.