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

generates a code of length 80 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+137x^68+92x^70+439x^72+468x^74+128x^75+989x^76+1152x^77+1252x^78+2816x^79+1542x^80+2816x^81+1184x^82+1152x^83+987x^84+128x^85+508x^86+334x^88+76x^90+106x^92+4x^94+49x^96+19x^100+3x^104+1x^108+1x^116

The gray image is a code over GF(2) with n=640, k=14 and d=272.
This code was found by Heurico 1.16 in 11.2 seconds.