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

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

Homogenous weight enumerator: w(x)=1x^0+102x^59+232x^60+496x^61+775x^62+1262x^63+1796x^64+2134x^65+3405x^66+4234x^67+4098x^68+4188x^69+3331x^70+2292x^71+1813x^72+1078x^73+602x^74+368x^75+218x^76+154x^77+66x^78+52x^79+29x^80+12x^81+9x^82+8x^83+4x^84+2x^85+3x^86+2x^87+1x^88+1x^94

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 21.1 seconds.