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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+48x^70+18x^71+120x^72+82x^73+176x^74+136x^75+361x^76+194x^77+580x^78+504x^79+1879x^80+1266x^81+2085x^82+1760x^83+1934x^84+1252x^85+1772x^86+498x^87+590x^88+198x^89+347x^90+136x^91+156x^92+74x^93+68x^94+20x^95+43x^96+6x^97+27x^98+26x^100+12x^102+6x^104+5x^106+3x^108+1x^112

The gray image is a code over GF(2) with n=664, k=14 and d=280.
This code was found by Heurico 1.16 in 11.8 seconds.