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

generates a code of length 35 over Z27 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+96x^67+144x^68+10x^69+78x^70+288x^71+8x^72+96x^73+6x^75+2x^87

The gray image is a code over GF(3) with n=315, k=6 and d=201.
This code was found by Heurico 1.16 in 0.02 seconds.