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

generates a code of length 85 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+83x^72+6x^74+205x^76+64x^78+285x^80+128x^81+132x^82+512x^83+323x^84+4864x^85+184x^86+512x^87+270x^88+128x^89+102x^90+185x^92+24x^94+87x^96+60x^100+23x^104+10x^108+3x^112+1x^132

The gray image is a code over GF(2) with n=680, k=13 and d=288.
This code was found by Heurico 1.16 in 3.54 seconds.