The generator matrix

 1  0  1  1  1  6  1  1 14  1 12  1  1  1  0  1 14  1  2 12  1  1  1  1  8  1  1 14  1  1  1  8  1  1  1  1 10 14  1  1  1  0  1  1  1  1  1  1 14  8  1  0  1  1  1  0  1  1  1  1  1  8  4  2  4  0  1  1  1  1  4  1
 0  1 11  6  1  1  0 11  1 14  1  5 15  0  1 14  1  5  1  1  7  6 13  4  1 15  6  1  5  0  6  1  2  5  6 15  1  1  8  5 10  1  9  2  0 12  6  3  1  1 11  1 14  2  5  1  5  5  1  0  9  1  1 12  8  1 13 10  6  2  4  3
 0  0 12  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  8  8 12  4 12  4  4  4 12 12  4  4 12  4 12  4  4  4  0  4  4 12  0  8  8 12  4  0 12 12  8 12  0  4 12 12 12  8 12  4  4  0 12  8  0  4
 0  0  0 12  0  0  0  0  8  4  8 12 12  4  4  0  4  8  4  4  4 12  4  8  8  8  4  4  8 12 12  0  0  8  8  4  8 12  0 12  0  0  4 12 12  4  8 12  0  8  4  4  0  8 12 12  0  8  0 12  0  8  8 12 12  0  4  4  4  8  0  0
 0  0  0  0  4  0  4  0  4  4 12  4  8 12  4  4 12  4  0  8  0  0  4  0 12  8  4 12  4 12  8  4 12  8  8  0  8  0  8  0  4  4  4  0  0 12  0  0  8  8  0  4  8  4  4 12  8 12  0  0  0  4  0  8 12  8  4  8  0 12  4  4
 0  0  0  0  0 12  4 12  8  4  4  0  4  0  0  8  4  4  0 12  8 12  4 12  0  0  8 12  8 12  0 12  4 12 12  8  4  4  8  0  8  0  0 12  4  8  8  4  0  4 12  0  8  0  0  4  8  4  8  4  4  0  0  4  0  4 12  0  8  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+170x^62+32x^63+538x^64+396x^65+1540x^66+1968x^67+3645x^68+4536x^69+7102x^70+8580x^71+8849x^72+8068x^73+7316x^74+4792x^75+3587x^76+1936x^77+1288x^78+372x^79+434x^80+40x^81+210x^82+79x^84+32x^86+17x^88+6x^90+1x^92+1x^96

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 62.2 seconds.