The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  0  2  1  1  1  1 12  1  2  2  0  1  8  2  1  1  1  2  1  1  2  1  2  1  1  1  1  0  2  1  2  0  1  1  8  1  1  1  2  1  1
 0  2  0  6  0  6  4  2  8 14  6  4 12  4 10  2  0  8  2  2  0  6 10  0  2 14  2  6 14  8  6 12  2 12 14  6  2  4  2  2 10  0 10  2 10  8 14  8 10 10  8 10  6  2 14  0  8  2 10 10  2  4  4  4 14  0  6
 0  0 12  0  0  0  4  0 12  0  0 12  8  0  8  8  8  8  4  4  4 12 12  4  4  4  0  0  4  8  4 12  0 12  8  0  0  4  0 12 12 12  0 12  0 12 12 12  0  8  8  4  8 12 12  8 12  4  0  8  0  8  8  8 12  0  4
 0  0  0 12  0  0  0  4  0  8  4  0  0  0 12  8 12 12  0 12 12  8 12 12  8  0  4 12  4  8  4  0 12  4  4  8  0  8  8  4  0  4  4  8  4  4 12 12  0  4 12  4 12  8 12  0 12  0  0 12  8  0 12  8  4 12  0
 0  0  0  0 12  0  0  8  4 12  4  4  4  8  4  4 12  8  8 12  0  4  0  0  4  8  4 12  4  4  8 12 12 12  0  8  8  0 12  4  4 12  8  8 12 12 12  0  0  8  4  8  8  4  0  8  4  4 12  4  4  0  8  8 12  4 12
 0  0  0  0  0  8  0  8  0  8  0  0  0  0  8  0  8  8  0  8  8  0  0  0  8  8  0  0  8  8  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  8  0  8  0  0  0  8  8  0  0  8  8  8  0  8  0  0  8  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  8  8  0  8  8  8  0  0  8  8  0  8  0  8  8  8  8  0  0  8  0  0  0  8  8  8  0  8  8  0  8  8  0  0  8  0  8  8

generates a code of length 67 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+78x^57+175x^58+234x^59+380x^60+646x^61+1103x^62+1160x^63+2975x^64+2432x^65+5651x^66+3296x^67+5637x^68+2346x^69+2946x^70+1202x^71+1083x^72+550x^73+296x^74+208x^75+135x^76+70x^77+58x^78+38x^79+24x^80+20x^81+10x^82+6x^83+4x^84+2x^85+1x^86+1x^96

The gray image is a code over GF(2) with n=536, k=15 and d=228.
This code was found by Heurico 1.16 in 64.5 seconds.