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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+74x^75+124x^76+128x^77+205x^78+210x^79+465x^80+300x^81+1232x^82+384x^83+2192x^84+336x^85+1195x^86+262x^87+437x^88+138x^89+121x^90+72x^91+73x^92+68x^93+46x^94+44x^95+33x^96+16x^97+14x^98+6x^99+3x^100+4x^101+2x^102+4x^103+2x^105+1x^130

The gray image is a code over GF(2) with n=672, k=13 and d=300.
This code was found by Heurico 1.16 in 18.7 seconds.