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

generates a code of length 34 over Z27 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+540x^60+54x^62+1196x^63+486x^64+324x^65+2784x^66+1944x^67+3564x^68+4266x^69+1944x^70+432x^71+1360x^72+564x^75+216x^78+6x^81+2x^90

The gray image is a code over GF(3) with n=306, k=9 and d=180.
This code was found by Heurico 1.16 in 0.944 seconds.