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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+74x^76+112x^77+172x^78+254x^79+294x^80+412x^81+596x^82+734x^83+1277x^84+1796x^85+2277x^86+2978x^87+3475x^88+3810x^89+3626x^90+3208x^91+2396x^92+1574x^93+1107x^94+742x^95+484x^96+356x^97+319x^98+210x^99+126x^100+116x^101+71x^102+58x^103+45x^104+14x^105+17x^106+8x^107+14x^108+2x^109+5x^110+5x^112+1x^114+1x^116+1x^122

The gray image is a code over GF(2) with n=712, k=15 and d=304.
This code was found by Heurico 1.16 in 43.4 seconds.