The generator matrix

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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+307x^72+660x^73+1236x^74+1348x^75+1885x^76+2140x^77+1948x^78+1704x^79+1815x^80+1292x^81+950x^82+472x^83+264x^84+116x^85+94x^86+56x^87+49x^88+16x^89+18x^90+4x^91+4x^92+2x^94+1x^100+2x^104

The gray image is a code over GF(2) with n=624, k=14 and d=288.
This code was found by Heurico 1.16 in 10.1 seconds.