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  2  1  0  2  1 12  1  1  1  1  2  0  1  1  1  2  1  1  1  1  1  1  1 12  1  1  1  1  1  2  1  1  0  1  2  1  1  1  1  1 12  2  1  1  1  1  0  1  1  1 12  2  0  1 12  1  1  1  4  1  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  4 10  0  6 14  8 12 10  0  6  6 12  2 10 10  2  6  2  0 12  6  2  6  0 12 10 10  0 10 14 10 10  2  2  0 12  6  6  8  6  0  2  2  4 10 12  0 10  6 10  2  6 10 10  8 14  2  2  2  6  2  6  2  8  2  8 10  8 12  2  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  8  0  8  8  0  0  8  8  8  8  8  8  0  8  0  8  8  0  0  0  0  0  0  0  8  8  0  8  8  8  8  8  8  8  8  8  0  8  8  0  8  0  0  8  0  8  0  8  8  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  8  8  8  0  8  8  0  0  0  8  0  8  8  8  0  0  8  0  8  8  8  0  8  8  8  0  8  0  8  0  0  8  0  0  0  8  8  0  8  8  8  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  8  0  8  8  0  0  0  8  8  8  8  0  0  8  0  8  8  8  8  0  0  8  0  0  8  8  8  8  0  8  8  0  0  0  0  8  0  8  8  8  0  0  0  0  8  0  8  8  8  0  0  8  8  8  0  0  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  0  8  8  0  0  8  0  8  8  8  0  0  8  8  8  8  8  0  8  8  0  0  0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  8  8  0  0  0  8  8  8  8  8  8  8  0  0  8  0  8  0  0  0  0  0  8  8  8  8  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  0  0  8  8  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  0  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8  8  0  8  8  0  8  8  0  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  8  8  0  0  8  8  0  8  8  8  0  8  8  8  8  0  8  8  8  0  0  8  0  0  0  8  0  8  8  8  0  8  0  0  8  8  0  8  0  0  0  0  8  8  8  0  8  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  0  0  8  0  0  0  8  8  8  0  0  0  8  8  8  8  8  0  8  8  8  8  0  0  8  0  0  0  0  8  8  0  8  8  8  0  0  0  8  0  8  0  0  0  8  0  8  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+19x^72+24x^73+64x^74+104x^75+126x^76+302x^77+236x^78+750x^79+563x^80+1520x^81+1263x^82+2388x^83+1676x^84+2472x^85+1252x^86+1536x^87+536x^88+692x^89+187x^90+324x^91+114x^92+106x^93+37x^94+18x^95+22x^96+4x^97+20x^98+12x^100+2x^102+3x^104+9x^106+1x^110+1x^130

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 8.81 seconds.