The generator matrix

 1  0  1  1  1  1 18  1  1  1 21  1  1  1  1 24  1  1 24  1  1  1  1  1  1  1 15  1  1  1  1  0  0  1
 0  1  1 26  7 18  1 17 25  3  1 20  4 26 21  1 15 16  1  1 24 20 24  2 20  4  1 20 23 23 26  1  1  0
 0  0 24  0  0 21 21 21  3 12 15 15  6 15  6  9 12  6  6 21  9  0 24  3  9  9 21 24  0  6  9  6  0 18
 0  0  0  9  0  9 18 18  9 18  0  9  0  9  0 18  0  9  9  0  9  9  0  9 18  9  9 18  0 18  0 18 18  0
 0  0  0  0  9  0 18 18 18  9 18  0  9 18 18 18  0  9 18  0  0 18  9  0  9  9  0  9  9 18  0 18  0  0

generates a code of length 34 over Z27 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+60x^58+66x^59+328x^60+342x^61+1008x^62+1610x^63+2574x^64+4146x^65+5932x^66+8220x^67+7782x^68+8630x^69+8382x^70+5652x^71+2888x^72+648x^73+210x^74+214x^75+180x^76+72x^77+56x^78+6x^79+18x^80+10x^81+10x^84+4x^87

The gray image is a code over GF(3) with n=306, k=10 and d=174.
This code was found by Heurico 1.16 in 4.32 seconds.