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

generates a code of length 79 over Z27 who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+106x^156+1944x^158+108x^159+26x^162+2x^237

The gray image is a code over GF(3) with n=711, k=7 and d=468.
This code was found by Heurico 1.16 in 0.283 seconds.