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  1  8  1  1  6  1  8  1  1  1 14  0  1  2  1  1  1  2  1  1 12 10  1  1  1  1  1  8  1  1  1  6  1  2 14  1  1  1  1  1  8  0  1  1  1  0  1  1  8  4  2  1  8  6  1  1  8  1  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 15  1  0 14  1  5  1  1  0 10  1  1  3  1  8  6  2  1  3 10  1  1  0 12  9  1  1  1  6  1 10  1 11  1  1 14  9 12  0  4  1  1 13  8 14  0  3 15  1  4 12  9  1  1 12  5  1  5  0
 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 12  4  4 12  4 12  4 12  4 12  4 12  4 12 12  4 12  0 12  8  4  4  0 12 12  8 12  8  4  0  0  4  4  8  4  4 12 12  8 12  8  0 12  8  4  0  0  4  8  8  0  4 12  4 12  4  0
 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 12  0  8  4 12  4  8  8  8 12  8  0 12 12 12 12  0  0 12 12 12  0  8 12 12  4  0  0 12  4 12  0  0  4  0  4  0  8  4  8 12 12 12  4  8  4  4  0  8 12  0  0  8 12  8 12  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  8 12 12  0  0  8  0  4  0  4 12  0 12  8  0  0 12 12  8  8  4  8  4  4  4 12  8  0  8  8  0  0 12  4  4  4 12  4 12  8  4  0 12 12  8 12  0 12 12 12  0  8  8  0  8  4 12 12  0
 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  4  8 12  0  4  8  4  8 12  0  8  0 12  0  8  0  4  8  4 12  8  4  4 12  4  8  8  8  4 12 12  0 12 12  4  4 12  8  8  4  0  0  0  4  0  4  0  8 12  4 12 12  0  4  8  4  0

generates a code of length 83 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+61x^72+120x^73+206x^74+518x^75+883x^76+1408x^77+2490x^78+3550x^79+5067x^80+6650x^81+7732x^82+8336x^83+7736x^84+6832x^85+5055x^86+3288x^87+2468x^88+1456x^89+663x^90+358x^91+235x^92+156x^93+89x^94+54x^95+50x^96+14x^97+14x^98+20x^99+10x^100+4x^101+5x^102+4x^103+1x^104+1x^106+1x^110

The gray image is a code over GF(2) with n=664, k=16 and d=288.
This code was found by Heurico 1.16 in 74.1 seconds.