The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  6  1  1  0  1 12  1  1  1  1 10  1  0  1  1  1  6  1 10  1 12  1  1  1  0  6  1  1 12  1  1  0  1  1  1  1 12 10  1  1  0  1  1  0  1  1  1  1  1 12 12  1  1 10  0  1  1  1  1  1  1  1  6 12  2  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  6  1  3  0  1  5  1 15 12 10  9  1  3  1  0  6  5  1 10  1 15  1  9 12  3  1  1  0  6  1  5 10  1  9 12 15 10  1  1  3 15  1  6  5  1  6  6 10  3 10  1  1  9  0  1  1 15  3  2 10 10 10  5  1  1 10  6  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  0  0  0  0  8  8  0  8  8  8  0  0  0  8  8  8  8  8  0  8  0  8  8  8  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  8  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  0  8  0  0  0  8  0  0  8  8  8  8  0  8  8  0  8  8  8  8  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  8  8  0  8  0  0  0  0  8  8  0  0  8  0  8  8  8  8  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  0  8  8  8  8  8  8  8  8  8  0  8  0  8  0  8  8  8  8  8  0  8  0  8  8  8  8  0  0  8  0  0  8  8  0  0  0  0  0  0  8  8  0  0  8  8  8  8  8  8  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  0  0  0  8  8  0  8  8  0  8  0  0  8  8  8  8  0  0  0  8  0  8  0  8  8  0  8  8  8  0  8  0  8  0  8  8  8  0  8  8  0  0  8  0  0  8  0  8  8  0  0  8  0  8  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  0  0  8  8  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  0  0  8  8  0  8  0  0  0  0  0  8  0  8  0  8  8  8  0  8  8  0  0  0  8  8  0  8  0  0  8  8  0  8  0  8  0  8  8  0  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  0  8  8  8  8  0  0  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  8  8  8  8  0  0  8  0  8  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  0  8  8  8  8  0  8  0  8  0  8  8  0  8  8  8  0  8  0  0  0  0  0  8  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  0  8  8  8  8  0  0  0  8  8  0  8  8  8  0  0  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  8  8  8  0  8  0  8  8  8  8  8  8  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  0  8  8  8  8  0  8  8  8  0  8  8  8  8  0  0  0  0  8  0  0  0  8  8  0  0  8  0

generates a code of length 82 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+29x^68+71x^70+58x^71+168x^72+160x^73+460x^74+444x^75+1530x^76+1438x^77+4230x^78+3776x^79+8537x^80+6392x^81+10983x^82+6416x^83+8594x^84+3812x^85+4169x^86+1426x^87+1462x^88+440x^89+457x^90+164x^91+103x^92+46x^93+62x^94+4x^95+32x^96+30x^98+15x^100+10x^102+8x^104+5x^106+1x^108+2x^110+1x^114

The gray image is a code over GF(2) with n=656, k=16 and d=272.
This code was found by Heurico 1.16 in 69.6 seconds.