The generator matrix

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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+38x^74+200x^75+557x^76+860x^77+1385x^78+2404x^79+3837x^80+5158x^81+6525x^82+7944x^83+8112x^84+7562x^85+6812x^86+5384x^87+3459x^88+2202x^89+1456x^90+700x^91+365x^92+224x^93+130x^94+86x^95+47x^96+22x^97+36x^98+10x^99+5x^100+2x^101+1x^102+6x^103+2x^105+1x^106+2x^107+1x^108

The gray image is a code over GF(2) with n=672, k=16 and d=296.
This code was found by Heurico 1.16 in 69.4 seconds.