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  0  4  1  1  1 12  1  8  1  1  1  1  1  1  1  1  2  1  1  2  2  1  4 12  1  1  1  1  1  2  1  1  2  2  1  4  4  2  2  2  1  1  0  2  1 12  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  6 10  4 12  4  2  4 14  4  6 10  8  4 10 14  0  2  2  2  0 10  8  8  2  6 12 10  4  6  2  0  2 14  6  0  8  6  2  2  2 10  0 12 10 12 14  4 10  6  6  2  4  2  2  0 10  8  0  2 12 12  8  0
 0  0  2  2 12  6  6  4  4  2  6  0  8 10  4 14 10  4  6  6 10  0  0  0 14 12  4 14 14  8 10  2  8 12  2 12 12  4 10  2  0 12  4 14 14 10  2  2 14  8  6  4 14  6  2  0 10  0 12 12 12  0  8 10  2  2  2  2  0 10  8  2 14  0  2  0
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  8  0  0  8  8  8  8  8  8  8  0  8  0  8  0  0  0  0  8  8  0  8  8  0  0  0  8  0  8  0  8  8  0  0  8  8  8  8  8  0  0  0  0  0  8  0  8  8  0  0  0
 0  0  0  0  8  0  8  0  8  8  0  0  0  8  0  0  8  8  0  0  8  0  8  8  8  0  8  0  8  0  0  8  8  8  0  8  0  8  8  0  0  0  0  0  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  8  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  8  0  0  0  0  8  8  0  8  8  0  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  0  8  0  8  0  8  8  8  0  8  8  0  0

generates a code of length 76 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+80x^69+260x^70+416x^71+450x^72+636x^73+881x^74+1010x^75+1074x^76+928x^77+774x^78+562x^79+344x^80+266x^81+192x^82+112x^83+74x^84+68x^85+32x^86+10x^87+8x^88+6x^89+3x^90+2x^91+2x^94+1x^112

The gray image is a code over GF(2) with n=608, k=13 and d=276.
This code was found by Heurico 1.16 in 1.78 seconds.