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

generates a code of length 36 over Z27 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+180x^68+96x^69+288x^70+288x^71+564x^72+324x^73+288x^74+30x^75+18x^77+36x^78+36x^79+18x^80+18x^83+2x^99

The gray image is a code over GF(3) with n=324, k=7 and d=204.
This code was found by Heurico 1.16 in 5.35 seconds.