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

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

Homogenous weight enumerator: w(x)=1x^0+88x^62+348x^63+614x^64+1214x^65+1394x^66+2490x^67+3271x^68+5004x^69+6028x^70+8352x^71+7993x^72+8428x^73+6043x^74+5186x^75+3249x^76+2338x^77+1357x^78+894x^79+442x^80+388x^81+174x^82+132x^83+43x^84+34x^85+19x^86+6x^87+2x^88+2x^89+1x^98+1x^100

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 79.7 seconds.