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

generates a code of length 69 over Z27 who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+226x^135+1782x^138+126x^141+50x^144+2x^207

The gray image is a code over GF(3) with n=621, k=7 and d=405.
This code was found by Heurico 1.16 in 0.151 seconds.