The generator matrix

 1  0  1  1  1  4  1  1  2 14  1  1  1  1  1 14  1  2  4  1  1  1  4  1  2  1  1  1 12  1  6  1  1 10  1  0  1  1  1  1  1  2  0  4  4  1 14  8  0  1  1  1  1  2  1  1  1 12  1  1  8  0  1  0  1  4  2  1
 0  1  1  0 11  1 14 15  1  1  2 13 11  4  1  1  0  1  1  9 10  6  1  5  1  7 13  0  1 10  1 15  2  1  3  1  4  2  4 10  7  1  1  1  2 13  1  2  0 15 14  8  9  0 10  1  1  1 14 14  4 12  0  0  0  1  8 15
 0  0  2  6  0  2  4 14  2  4 14  0  0  6  8  8  0 10  2  6  2  0  0  6 12  6  4  4 10  6  2  0  8 10  2  6  2  2  4 12  6  8  4  4  2  0  4 10  2  4 12 10 12  2 12  6  0 10  2  0  2  2 10  2 10  6 10 10
 0  0  0 12  0  0  0  0  8  0  4  0 12  8  4  0  4 12 12 12  8  4  4 12  4 12  8  8  0  4  8 12  0 12  0 12  8  4  8 12  0 12  4  8  0  8  4 12  4  4  4 12  0 12  0 12 12  8  8 12  0 12  8  4  4  0  8  4
 0  0  0  0 12  0  8  8  8  0  0  4  0  4  0 12  4 12  4 12  4  4  8  4 12  8  0  4 12 12  4  4  4  8 12  8  0 12  8  4 12 12  8  4  4  0  4  4  0  4  8  4  0  0  8  4  8 12  8  8  8  8  8 12  8  0 12  8
 0  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  8  8  8  8  0  8  0  8  0  8  8  0  0  8  0  0  0  0  8  8  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  0  0  0  0  8  0  0  8  0  0  8  8  0

generates a code of length 68 over Z16 who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+74x^59+324x^60+746x^61+1217x^62+2364x^63+3333x^64+5414x^65+6502x^66+8634x^67+8083x^68+9138x^69+6544x^70+5486x^71+3175x^72+2182x^73+1112x^74+562x^75+291x^76+158x^77+99x^78+26x^79+19x^80+24x^81+14x^82+6x^83+6x^84+2x^85

The gray image is a code over GF(2) with n=544, k=16 and d=236.
This code was found by Heurico 1.16 in 53.2 seconds.