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

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

Homogenous weight enumerator: w(x)=1x^0+92x^59+267x^60+570x^61+850x^62+1442x^63+1806x^64+2254x^65+3316x^66+3780x^67+4085x^68+3864x^69+3270x^70+2568x^71+1671x^72+1148x^73+724x^74+462x^75+260x^76+144x^77+80x^78+34x^79+34x^80+18x^81+12x^82+6x^83+4x^84+2x^85+4x^86

The gray image is a code over GF(2) with n=544, k=15 and d=236.
This code was found by Heurico 1.16 in 21.4 seconds.