The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+352x^72+1778x^73+2884x^74+4580x^75+5372x^76+6860x^77+7095x^78+7906x^79+7232x^80+7278x^81+5301x^82+4166x^83+2203x^84+1296x^85+611x^86+366x^87+141x^88+52x^89+27x^90+22x^91+9x^92+2x^94+2x^96

The gray image is a code over GF(2) with n=632, k=16 and d=288.
This code was found by Heurico 1.16 in 43.8 seconds.