The generator matrix

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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+31x^74+98x^75+199x^76+468x^77+637x^78+1320x^79+1791x^80+2876x^81+3106x^82+3976x^83+3962x^84+4030x^85+3036x^86+2828x^87+1798x^88+1266x^89+523x^90+360x^91+144x^92+102x^93+66x^94+42x^95+30x^96+18x^97+18x^98+14x^99+6x^100+8x^101+2x^102+2x^103+4x^104+2x^106+1x^108+3x^110

The gray image is a code over GF(2) with n=672, k=15 and d=296.
This code was found by Heurico 1.16 in 19.8 seconds.