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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+48x^73+116x^74+194x^75+242x^76+288x^77+441x^78+584x^79+879x^80+1296x^81+1751x^82+2352x^83+2930x^84+3434x^85+3663x^86+3504x^87+3102x^88+2414x^89+1676x^90+1174x^91+775x^92+520x^93+425x^94+284x^95+197x^96+160x^97+95x^98+88x^99+40x^100+30x^101+21x^102+12x^103+18x^104+2x^105+2x^106+5x^108+2x^110+3x^112

The gray image is a code over GF(2) with n=688, k=15 and d=292.
This code was found by Heurico 1.16 in 41.9 seconds.