The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  8  1  1  2 12  4  1  2  1  1  1  0  1  1  1  1  2  8  1  1  4  1  1  1  2  1  2  1  2  1  1  1 12  0  1  1  0  1  2  2  4  1 12  4  2  1  1  2  1  2 12  0  2  1
 0  2  0  6  4 14 12  2  0  6  6 12  2  8  4 10  8 10  4 14  8 10  6  8  2  6  2 10  4 14  2 12  6  2  2  2  8 10  0 14  4  2  0  2  2  6 14  2  0  4  2 14  8 12  2  6  4 10  2  2  4  8  2  0  0  2  2  6 14  2  4 10  2  2  2  8 14  4  8  6  2  0 12  6
 0  0 12  0  4  4  0  4  0  0 12  8  4  4 12  8  8  4  0 12 12  8  0  4  4  0  0  8 12  4  4  0  8 12  8 12 12  8  0 12  4  8  4  4  0  8 12  4  4  0 12  8  8  8  4  8  4  4  4 12 12  0  0  4  8  8  8  4 12  4 12  0  8  4 12  4  0 12  4  0  0  4  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  0  0  8  0  8  8  8  8  0  8  8  8  8  0  8  0  0  0  8  8  8  8  0  8  0  8  0  0  0  0  0  0  0  0  8  8  0  0  8  0  8  8  0  8  0  0  0  8  0  0  8  0  0  0  8  8  0  0  0  0  8  8  8  8  0  8  8  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  0  8  0  8  8  0  8  8  8  8  0  8  8  8  8  0  8  0  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  8  8  0  0  8  8  8  0  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  0  8  8  0  8  8  0  0  8  0  0  8  8  0  8  8  0  0  0  8  0  0  8  8  0  8  0  8  8  8  8  0  0  0  8  8  0  0  8  0  8  8  0  8  0  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  8  0  8  0  0  0  8  8  8  0  0  8  0  8  0  8  0  8  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  0  0  8  8  0  8  8  8  8  0  8  0  0  8  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  0  8  0  8  0  8  8  0  0  8  0  8  8  0  0  8  8  0  8  8  8  0  0  8  8  0  0  0  0  0  8  0  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  0  8  0  8  8  8  8  8  0  8  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  0  0  8  8  0  0  8  0  0  8  8  8  0  8  0  0  8  8  8  0  8  8  8  0  8  0  0  0  8  0  8  0  0  0  8  0  0  0  8  8  8  8  8  0  8  0  8  8  8  8  0  0  8  8  0  0  8  0  0  0  0  8  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+57x^72+58x^73+132x^74+262x^75+367x^76+620x^77+703x^78+1544x^79+1301x^80+3168x^81+2281x^82+4588x^83+2771x^84+4656x^85+2189x^86+3166x^87+1285x^88+1486x^89+635x^90+594x^91+298x^92+224x^93+139x^94+72x^95+46x^96+24x^97+47x^98+12x^99+11x^100+4x^101+12x^102+2x^103+6x^104+1x^106+1x^108+4x^110+1x^118

The gray image is a code over GF(2) with n=672, k=15 and d=288.
This code was found by Heurico 1.16 in 32.1 seconds.