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

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

Homogenous weight enumerator: w(x)=1x^0+49x^72+56x^73+113x^74+126x^75+275x^76+252x^77+349x^78+350x^79+421x^80+1294x^81+590x^82+4068x^83+623x^84+4076x^85+539x^86+1340x^87+450x^88+328x^89+290x^90+194x^91+149x^92+120x^93+98x^94+50x^95+65x^96+18x^97+42x^98+12x^99+9x^100+20x^102+4x^103+5x^104+5x^106+1x^110+1x^112+1x^118

The gray image is a code over GF(2) with n=672, k=14 and d=288.
This code was found by Heurico 1.16 in 11.3 seconds.