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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+58x^58+324x^59+521x^60+1124x^61+1357x^62+2340x^63+3183x^64+4858x^65+6667x^66+7572x^67+9223x^68+7964x^69+6723x^70+5086x^71+3214x^72+2168x^73+1202x^74+890x^75+447x^76+304x^77+110x^78+102x^79+40x^80+30x^81+9x^82+6x^83+9x^84+1x^86+2x^88+1x^94

The gray image is a code over GF(2) with n=544, k=16 and d=232.
This code was found by Heurico 1.16 in 74.6 seconds.