The generator matrix

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

generates a code of length 39 over Z27 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+378x^68+810x^69+4206x^70+5880x^71+11278x^72+18654x^73+23724x^74+37114x^75+54216x^76+55890x^77+68524x^78+86388x^79+59586x^80+48052x^81+31794x^82+14364x^83+6932x^84+2844x^85+468x^86+38x^87+180x^88+90x^89+24x^90+6x^91

The gray image is a code over GF(3) with n=351, k=12 and d=204.
This code was found by Heurico 1.16 in 283 seconds.