The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  6  1  1  0  1  1  1 12  1 10  1  1  0  1  6  1  1  1  1  1  1 12 10  1  1  6  1  0  1  1  1 12  1  1  1 10  0  1  1  1  1  0  1  1  1  6  1  1 10  1  6  1  1 10 10  1  1  1  1  1  1  1  6  1  1  2  1  1  0  0  0  1
 0  1  3  6  5  1 12  7  1 10  9  1  6  1  3  0  1  5 12  9  1 10  1 15 15  1  6  1  5  0 12  3  9 10  1  1  3 12  1  5  1  6 10  0  1  9  0 15  1  1  3 12  5 10  1  9  0  6  1  9  6  1  5  1 15  3  1  1  9 10  8  9  6  1 10  1 12  0  1  9 12  1  1  2  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  0  0  8  8  0  8  8  0  0  0  8  8  8  8  0  8  0  0  8  8  0  8  0  8  0  0  8  8  8  0  8  0  0  8  0  8  8  8  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  0  8  0  0  0  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  0  0  8  8  8  0  0  0  8  0  0  8  8  0  8  0  8  0  8  8  0  0  0  8  0  0  0  0  0  8  8  0  0  8  8  8  0  8  8  0  8  8  8  8  0  8  0  0  8  8  0  8  8  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  8  8  8  8  8  0  8  8  8  8  0  8  0  8  8  8  8  8  8  8  0  8  8  8  8  8  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  0  8  0  0  8  8  8  8  0  8  8  8  0  0  8  0  8  0  8  8  0  0  0  8  0  8  8  8  8  8  0  0  0  0  0  0  0  0  8  8  0  0  8  0  8  8  8  0  0  8  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  8  8  0  8  8  8  8  8  0  0  0  8  0  0  8  8  8  8  8  0  0  8  0  0  8  0  8  0  0  8  0  8  8  0  8  8  8  8  0  8  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  0  0  8  0  0  8  0  8  8  8  8  8  0  0  0  8  8  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  0  0  0  0  8  8  8  0  8  0  8  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  8  8  8  0  8  0  8  0  8  0  0  8  8  8  0  8  0  0  8  0  0  0  0  8  8  0  0  8  8  0  0  8  8  8  8  8  0  8  8  8  0  8  8  0  8  8  0  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  0  0  8  0
 0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  0  8  0  0  8  8  0  0  0  0  8  0  0  8  0  0  8  8  0  8  8  0  0  8  8  0  8  0  8  0  0  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+75x^72+26x^73+85x^74+128x^75+185x^76+450x^77+645x^78+1218x^79+2359x^80+2848x^81+6045x^82+5274x^83+10106x^84+6724x^85+10134x^86+5284x^87+6013x^88+2842x^89+2285x^90+1252x^91+635x^92+410x^93+165x^94+154x^95+53x^96+12x^97+50x^98+2x^99+12x^100+28x^102+10x^104+12x^106+6x^108+4x^110+1x^112+3x^114

The gray image is a code over GF(2) with n=680, k=16 and d=288.
This code was found by Heurico 1.16 in 74.4 seconds.