The generator matrix

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

generates a code of length 35 over Z27 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+456x^61+318x^62+1842x^63+3846x^64+4662x^65+9560x^66+11892x^67+15582x^68+22922x^69+24996x^70+25782x^71+24038x^72+16410x^73+7374x^74+4840x^75+2004x^76+186x^77+190x^78+162x^79+36x^80+30x^81+12x^82+6x^83

The gray image is a code over GF(3) with n=315, k=11 and d=183.
This code was found by Heurico 1.16 in 30.9 seconds.