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  3  1  3  1  1  3  9  9  3  1  3  1  1  1  3  3  1  1  1  1  3  9  3  3  0  3  3  3  1  3  9  9  0  3
 0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9  9 18 18  0  0  9  9  9  9 18 18  0  9  9 18 18  0  9 18  9 18  0 18  9  0  9 18  0  0  0 18  9  0

generates a code of length 68 over Z27 who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+60x^137+4x^138+12x^140+4x^141

The gray image is a code over GF(3) with n=612, k=4 and d=411.
This code was found by Heurico 1.16 in 0.743 seconds.