The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+25x^62+128x^63+360x^64+762x^65+1382x^66+2214x^67+3559x^68+5072x^69+6979x^70+8024x^71+8423x^72+8534x^73+6697x^74+5302x^75+3653x^76+1792x^77+1190x^78+662x^79+344x^80+194x^81+91x^82+52x^83+30x^84+24x^85+18x^86+2x^87+12x^88+6x^89+2x^90+2x^92

The gray image is a code over GF(2) with n=576, k=16 and d=248.
This code was found by Heurico 1.16 in 56.7 seconds.