The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+197x^72+216x^73+780x^74+792x^75+1616x^76+1512x^77+2348x^78+1616x^79+2334x^80+1512x^81+1534x^82+792x^83+673x^84+216x^85+136x^86+42x^88+20x^90+26x^92+12x^94+4x^96+2x^98+2x^104+1x^108

The gray image is a code over GF(2) with n=632, k=14 and d=288.
This code was found by Heurico 1.16 in 5.52 seconds.