The generator matrix

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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+233x^72+228x^73+746x^74+764x^75+1691x^76+1488x^77+2248x^78+1708x^79+2289x^80+1448x^81+1640x^82+836x^83+608x^84+160x^85+164x^86+20x^87+35x^88+4x^89+22x^90+25x^92+4x^94+8x^96+8x^98+4x^100+2x^104

The gray image is a code over GF(2) with n=632, k=14 and d=288.
This code was found by Heurico 1.16 in 9.01 seconds.