The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+133x^72+734x^73+982x^74+2066x^75+1476x^76+2612x^77+1697x^78+1894x^79+1165x^80+1472x^81+699x^82+762x^83+245x^84+256x^85+95x^86+46x^87+19x^88+14x^89+13x^90+1x^92+1x^94+1x^102

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 3.26 seconds.