The generator matrix

 1  0  0  1  1  1 10  2  1  4  1  1  1 10  1  4  1  4  1 14  1 10  1  1  1  8  1  1  6  1  4  6 10  1 12  1  1  1  8  1 14  1  1  4  1  1  1  6  4  8 10  1  1  1 12  1 10  8  1 12  1  1  1 10  1  1  1  4 14  1  1 12  1  1  1 12  1  1  1  1  1 12  8  1 14 12  1  1  6 12  1  6  1  6  1  1
 0  1  0  0  5 13  1  6  2  1 15 15  6  1  7  6  0  1 13  1  8  8 15 10  1  1 12 10  1  1  1  8  1 13  8  4  2 13  1  5  1  3 14  2 12  6  7  1  1  1 14  8  3  4  1 11  1  1 12  1 11 11 13  6 12  3 10  1  1  1  9  4  9  4 15 12  0  9  9  4 12  1 14 14  1  1  8  2 12  1  6  1  6  1 10  6
 0  0  1 11  7  4  7  1  5  5  6 11  0  8 12  1  1  2 13  5 10  1  1  7 14 13  0 14  2  4  3  1 12  9  1  2  7  2 11  3 14  7 13  1  4 10  6  4  8  7  1 10  1 11 13 11  7  0  7  6 12  8 12  1  9 15  6  2  9  3 11  1  0  8 13  1  7  0  6 13  9  1  1 12  0  7 11  1  1  1 15  2  2 10 10  2
 0  0  0 12  4  0  4 12 12  4  0  4  8  8  8 12 12  0 12  4  0  4  4 12  0 12  8  8  0  8  4 12  8 12  8  0  0  4  0  8  4  8  8  8 12 12  4 12  0  0  0 12  0  8  0  0  0  4  4  0 12  4  4  8  0  4  4 12 12 12  0  8  4 12  8  4  0  8 12  8  0  4  8 12  0  4  8 12  8  0  4  0  8 12  0  4
 0  0  0  0  8  0  8  8  8  0  8  0  8  8  8  0  8  0  0  8  8  8  8  0  0  0  0  8  8  0  0  0  0  8  8  0  8  0  8  0  0  8  0  0  0  8  8  8  8  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  8  8  0  8  8  0  8  0  8  8  0  8  8  8  8  8  0  8  8  8  0  8  8  0  8  8  8  0  0  0  8  8

generates a code of length 96 over Z16 who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+300x^89+1006x^90+1712x^91+2624x^92+2660x^93+3285x^94+3232x^95+3917x^96+3132x^97+3333x^98+2358x^99+2028x^100+1342x^101+869x^102+442x^103+227x^104+116x^105+62x^106+38x^107+26x^108+18x^109+16x^110+6x^111+9x^112+5x^114+4x^115

The gray image is a code over GF(2) with n=768, k=15 and d=356.
This code was found by Heurico 1.16 in 17.3 seconds.