The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+33x^72+352x^73+606x^74+1026x^75+670x^76+1110x^77+985x^78+1068x^79+609x^80+768x^81+352x^82+274x^83+130x^84+74x^85+56x^86+24x^87+4x^88+28x^89+8x^90+8x^91+4x^93+1x^102+1x^104

The gray image is a code over GF(2) with n=624, k=13 and d=288.
This code was found by Heurico 1.16 in 1.35 seconds.