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

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

Homogenous weight enumerator: w(x)=1x^0+78x^62+402x^63+678x^64+1018x^65+1588x^66+2490x^67+3167x^68+5676x^69+6035x^70+7732x^71+7627x^72+8464x^73+6063x^74+4948x^75+3325x^76+2638x^77+1397x^78+1020x^79+518x^80+274x^81+184x^82+102x^83+44x^84+34x^85+13x^86+10x^87+8x^89+1x^90+1x^94

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 80.6 seconds.