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

generates a code of length 34 over Z27 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+168x^64+150x^65+206x^66+324x^67+570x^68+336x^69+252x^70+36x^71+20x^72+30x^73+48x^74+2x^75+18x^76+6x^77+18x^79+2x^93

The gray image is a code over GF(3) with n=306, k=7 and d=192.
This code was found by Heurico 1.16 in 0.398 seconds.