The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+173x^72+360x^73+497x^74+788x^75+775x^76+1068x^77+1025x^78+920x^79+715x^80+912x^81+489x^82+276x^83+116x^84+28x^85+25x^86+7x^88+6x^90+2x^94+4x^98+4x^100+1x^108

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 1.52 seconds.