The generator matrix

 1  0  1  1  1  6  1  1 14  1 12  1  1  1  0  1  2  1  1 14  1 12  1  1  1  8  1  1  6  1  1  1  1  6  1  4  1  2  0  1  1  6  1  4  1  1  1  1  1  1 10  8  1  1  1 14  1  1  1  1  1 12  8 12  1  0 14  1  1  0  4  1  1  2  1  1  1  1  1  2  1  1
 0  1 11  6  1  1  0 11  1 14  1  5 15  0  1 14  1  5 12  1  5  1 14  7 11  1  0  6  1 10 13  3  4  1 13  1  4  1  1 14 11  1  5  1 12  1  5  2 12 15  1  1 14  6  3  1 12 11 14  9  4  1  1  1 10  4  1  2  5  1  1  7 14  1  0 15  0  9 13  1  6 14
 0  0 12  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 12  8  8  4  4  4  4 12 12 12 12 12 12 12 12  4  4 12 12  4 12 12  4  4  0 12 12  0  4  4 12 12 12  0 12  4 12  8  8 12  8  4  4  4  0  8  8  4  8  4  4  0
 0  0  0 12  0  0  0  0  8  4  8 12 12 12 12  0 12  8  4 12  8 12  0  4  4 12  4  0  8  4 12 12  4  0  4  4  0 12  0  8 12 12  8 12  8  8  8 12 12  8  4  8  8 12 12  8  0  8 12  8  4  0  8 12  8  8  8  8 12  4  4 12 12  4  0  8  8  8  8  0  8  8
 0  0  0  0  4  0  4  0  4  4 12  4  8  0  0  8  4  8 12  8  4  4  4  8 12 12 12  8 12  0  0 12  4  8  4  8 12 12  4  0 12 12 12  0  4 12 12  4  4  0 12  0  8  0  4  0  0 12  4 12  0 12  4  0  8  4  4  4  0  4 12 12  8  0  8  8  4  4  8 12  4  0
 0  0  0  0  0 12  4 12  8  4  4  0  4 12  4 12  4  0  8  8  4  0  8  0 12 12  8  0 12 12 12  8  4  4  8  4  4  8  0  8 12  0  4  0  8 12  0 12  0 12  4  8  0  0  4 12 12  4  0  8  4  8  0  8  8  4 12  8  4 12  4  0  0 12  4  0 12  4  0 12  0 12

generates a code of length 82 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+223x^72+52x^73+584x^74+452x^75+1729x^76+1948x^77+3692x^78+4896x^79+6790x^80+7976x^81+9022x^82+8068x^83+6577x^84+4892x^85+3928x^86+1944x^87+1417x^88+428x^89+456x^90+64x^91+195x^92+118x^94+47x^96+22x^98+8x^100+2x^102+1x^104+3x^108+1x^112

The gray image is a code over GF(2) with n=656, k=16 and d=288.
This code was found by Heurico 1.16 in 89.6 seconds.