The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1290x^61+2382x^62+4664x^63+11328x^64+15042x^65+25340x^66+38118x^67+47280x^68+65990x^69+77616x^70+76032x^71+68638x^72+52110x^73+25344x^74+12442x^75+5982x^76+1500x^77+70x^78+150x^79+84x^80+2x^81+30x^82+6x^83

The gray image is a code over GF(3) with n=315, k=12 and d=183.
This code was found by Heurico 1.16 in 251 seconds.