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

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

Homogenous weight enumerator: w(x)=1x^0+108x^60+60x^61+18x^62+212x^63+264x^64+108x^65+736x^66+744x^67+1674x^68+1284x^69+762x^70+144x^71+162x^72+78x^73+108x^75+30x^76+42x^78+6x^79+8x^81+6x^87+4x^90+2x^93

The gray image is a code over GF(3) with n=306, k=8 and d=180.
This code was found by Heurico 1.16 in 0.131 seconds.