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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+82x^72+274x^73+301x^74+574x^75+689x^76+930x^77+975x^78+936x^79+845x^80+866x^81+522x^82+458x^83+233x^84+210x^85+118x^86+62x^87+42x^88+20x^89+17x^90+16x^91+9x^92+4x^93+3x^94+2x^95+2x^96+1x^116

The gray image is a code over GF(2) with n=632, k=13 and d=288.
This code was found by Heurico 1.16 in 2.04 seconds.