The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^72+692x^73+1386x^74+2168x^75+3036x^76+3484x^77+4059x^78+4120x^79+3482x^80+3256x^81+2724x^82+1718x^83+1122x^84+680x^85+314x^86+204x^87+98x^88+28x^89+42x^90+30x^91+6x^92+4x^93+3x^94+1x^96

The gray image is a code over GF(2) with n=632, k=15 and d=288.
This code was found by Heurico 1.16 in 12.8 seconds.