The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+398x^72+520x^73+1066x^74+780x^75+971x^76+1056x^77+886x^78+720x^79+810x^80+456x^81+338x^82+28x^83+71x^84+16x^85+34x^86+8x^87+18x^88+12x^90+1x^92+1x^104+1x^108

The gray image is a code over GF(2) with n=616, k=13 and d=288.
This code was found by Heurico 1.16 in 41.9 seconds.