The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  6  1  1  1  0 12  1  1  1 10  1  1  1  0  1  1  6 12  1  1  1  1 10  1  1  0  1  1  6 10 12  1  1  1  1  1  1  1  0  6  1 12  1  1  0  1  1 10  1  1  1  1  1 12  1  6 10  6  1  1  1  1  1  1 10  1  6  1  0 10  2
 0  1  3  6  5  1 12  7  1 10  9  1  6  1  3  0  5  1  1 12 15  9  1 10  0  3  1  5 10  1  1 15 12  9  6  1  5  3  1  6  0  1  1  1 10 15  9 12  0 15  3  1  1  6  1  5 10  1 15  6  1  0 12 15  9 12  1  5  1  1  1 15 10  5  5  3  0  1  3  1 15  1  1  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  8  0  8  0  0  8  8  8  8  8  0  8  0  0  8  8  0  8  0  0  0  0  8  8  0  0  0  0  0  8  8  8  0  8  0  8  0  0  8  0  8  0  8  0  8  0  0  0  8  8  8  8  0  8  8  8  8  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  0  0  8  8  0  8  8  8  8  8  0  8  0  8  0  0  8  8  0  8  8  8  8  8  8  0  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  0  0  8  8  0  0  0  0  8  8  0  0  0  8  8  8  8  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  8  8  8  8  8  8  0  8  0  0  8  8  0  0  8  0  8  8  8  0  8  8  8  8  0  8  8  8  8  8  8  8  0  8  0  8  0  0  0  0  0  0  8  0  8  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  0  0  8  0  0  0  8  8  8  0  8  8  0  8  0  8  0  0  0  0  0  8  8  0  0  8  0  8  8  0  8  0  8  8  0  0  8  8  8  0  8  0  8  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  0  8  8  8  8  0  0  0  8  8  8  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  0  8  0  8  8  0  8  0  0  0  0  8  0  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  8  0  0  0  0  8  8  8
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  8  8  0  0  8  8  0  0  0  0  8  0  0  8  8  8  0  0  8  8  0  0  0  8  0  8  0  8  8  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  0  8  0  0  8  8  0  0  0  0  8  8  0  8  0  0  8  0  0  8  8  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  8  8  0  8  8  8  0  0  8  0  0  0  8  8  0  0  8  0  8  8  0  0  8  0  0  0  8  0  0  8  0  8  8  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  0  0  8  0  8  8  0  8  0  8  0  0  8  0  8  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  0  0  8  8  0  8  0  8  0  8  0  0  8  8  0  8  0  8  0  0  8  0  0  0  0  0  0  8  0  0  8  0  0  8  0  8  8  8  8  0  8  0  0  8  8  0  8  0  0  8  8  8  8  0  8  0  8  8  8  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+133x^72+162x^74+48x^75+621x^76+472x^77+1422x^78+1568x^79+4189x^80+4288x^81+7876x^82+6912x^83+10200x^84+6960x^85+7916x^86+4320x^87+4102x^88+1536x^89+1402x^90+464x^91+547x^92+56x^93+166x^94+93x^96+47x^100+25x^104+8x^108+1x^112+1x^116

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 97.3 seconds.