The generator matrix

 1  0  0  0  1  1  1 18  1  1  1  1  1 21  1  1  6  1  1  1 12  1  1 24 18  1  1 12  1  1  1  6  1  1
 0  1  0  0 18  1 19  1  3 12 11 23  2  1 21  6  1 19 25 11  1 17 12  3  1 25 16  1 10  8 13 24  7  0
 0  0  1  0 16 25 14  7  4  5 15  1 11  8 24  5  6  4  2 10  7  3 18  1 10  0 19 11 20  5  2  1  0 13
 0  0  0  1 14  9  5  5  1 21 13  3 11 22 26  4 13  7 16 17 16  0 13  4  3  1 14 20  8 16 10 20 20 14

generates a code of length 34 over Z27 who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+1092x^59+1706x^60+5694x^61+10590x^62+12736x^63+27942x^64+36624x^65+44054x^66+75354x^67+75660x^68+69170x^69+78156x^70+49866x^71+22204x^72+13944x^73+5316x^74+944x^75+102x^76+162x^77+80x^78+12x^79+24x^80+6x^81+2x^84

The gray image is a code over GF(3) with n=306, k=12 and d=177.
This code was found by Heurico 1.16 in 242 seconds.