The generator matrix

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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+178x^68+542x^69+1413x^70+2480x^71+4107x^72+5086x^73+6995x^74+7594x^75+8880x^76+7734x^77+7451x^78+4908x^79+3683x^80+2108x^81+1196x^82+582x^83+282x^84+134x^85+80x^86+48x^87+17x^88+8x^89+12x^90+4x^91+4x^92+2x^93+4x^94+2x^97+1x^98

The gray image is a code over GF(2) with n=608, k=16 and d=272.
This code was found by Heurico 1.16 in 48.7 seconds.