The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+534x^60+162x^62+1288x^63+486x^64+972x^65+2952x^66+1944x^67+1944x^68+3770x^69+1944x^70+1296x^71+1480x^72+738x^75+140x^78+30x^81+2x^87

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 33.9 seconds.