The generator matrix

 1  0  1  1  1  1  1 18  1  1  1  3  1 24  1  1  0  3  1  1  1 24  1  1 21  1 12  1  1  1 12  0  1  1
 0  1  1 26 21 20 16  1 24 23  4  1 26  1 20 23  1  1  0  4 17  1 16  1  1 19  1  0 17 18  1  1 10  1
 0  0 24  0 18 18 15  3  0 18 24  3 15 18 24 15 24 12  6  0 12 15  0 21 24 18  6 24 12  3 18 12  3  3
 0  0  0  9  9  0 18  9 18 18  9 18  9  9 18  0  9  0  9  9  0 18  0  9  0 18 18  0 18  9 18  9  0 18

generates a code of length 34 over Z27 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+246x^61+246x^62+536x^63+1524x^64+528x^65+1770x^66+4368x^67+834x^68+2992x^69+4458x^70+690x^71+732x^72+474x^73+66x^74+28x^75+96x^76+66x^77+14x^78+12x^79+2x^84

The gray image is a code over GF(3) with n=306, k=9 and d=183.
This code was found by Heurico 1.16 in 0.987 seconds.