The generator matrix

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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+60x^72+72x^73+130x^74+416x^75+456x^76+1050x^77+1296x^78+3250x^79+2712x^80+6444x^81+4828x^82+9174x^83+5681x^84+9400x^85+4758x^86+6440x^87+2930x^88+3180x^89+1090x^90+1104x^91+359x^92+294x^93+137x^94+86x^95+60x^96+32x^97+32x^98+10x^99+23x^100+8x^101+8x^102+4x^104+8x^106+1x^108+1x^110+1x^112

The gray image is a code over GF(2) with n=672, k=16 and d=288.
This code was found by Heurico 1.16 in 74.2 seconds.