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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1  1  2  4  1  2  2  2  1  4  1  1  2  4  2  2  2  4  8  8  1  1  2  2  2  0  1  1  4  2  1  4  8  1  1  1  1  2  1
 0 12  0  0  0  4 12  4  0  8  0 12  0  0 12 12  4  4 12  0  8  8  4  4  8 12  0  4  4 12  8  8  4  8 12 12  8  8 12  8  0  0  0  0 12 12  4  0 12  0  4  8  8  0  8  0  4 12 12 12  0  8 12  4  4  0  0  4 12  4  0 12  0  0 12  4 12  4  8  8  8  8  4  4
 0  0 12  0  4  4 12  0  0  0 12  8  0 12  4  0 12  8  4 12  8 12  8 12  0  4 12  8  0  8  4  8  4  8 12  0  0  0  4 12  8  4 12 12  8  0  8  4  8  4  8 12 12  0 12  4  8 12  0  8  8  0 12 12  8  4  0  0  4  0  0  0  4  8  0 12  4  8  0  4 12  8  4  4
 0  0  0 12  4  0 12  4  0  4 12 12  8  8  4  8  0  0  4  4  4  8  4  4  0  0  8  8  4  8  4 12  0 12  8  4 12 12  4  4  4  4 12  8  0  4  8 12  0  4 12  4  4  4 12  4 12  4  0  0  4  4  4  8  4  4  0  8  8 12  4  8  0  4  4 12  4 12  8 12  0  4  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  0  0  0  8  8  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  8  0  8  8  0  8  8  8  8  8  8  8  0  0  8  0  0  0  8  8  0  8  0  0  0  8  8  0  0  0  0  8  8  8  0  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0  0  8  8  8  0  0  8  0  0  8  8  0  8  8  0  8  8  0  0  8  0  0  0  0  8  0  8  8  0  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  8  0  0  0  8  8  0  8  8  0  8  8  8  8  8  8  8  8  0  8  8  0  0  0  8  0  8  0  0  0  8  8  0  8  8  8  8  0  0  8  0  8  8  0  0  0  8  0  8  0  0  8  0  8  0  0  0  0  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  0  0  8  8  8  8  8  0  8  8  0  8  8  0  0  8  8  0  0  8  8  0  8  8  8  0  8  8  0  0  8  8  8  0  8  8  0  8  0  0  8  8  8  0  8  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  8  8  8  0  8
 0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  8  8  0  0  8  8  0  8  0  8  0  8  0  8  8  0  0  8  8  8  0  0  0  8  0  8  0  0  8  8  8  8  8  8  8  0  8  0  8  0  8  0  8  0  0  8  8  0  8  0  8  0  8  8  0  0  8  8  0  8  0  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+202x^72+416x^74+44x^75+829x^76+152x^77+1098x^78+564x^79+2069x^80+1616x^81+3400x^82+3736x^83+4455x^84+3776x^85+3616x^86+1672x^87+2045x^88+560x^89+1028x^90+124x^91+599x^92+40x^93+334x^94+4x^95+227x^96+84x^98+50x^100+8x^102+15x^104+2x^108+1x^112+1x^116

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 40.7 seconds.