The generator matrix

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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+87x^68+68x^70+32x^71+599x^72+144x^73+1274x^74+896x^75+3223x^76+2848x^77+6204x^78+5152x^79+9122x^80+6336x^81+8940x^82+5344x^83+6388x^84+2784x^85+3028x^86+832x^87+1306x^88+176x^89+426x^90+32x^91+170x^92+28x^94+53x^96+33x^100+7x^104+3x^108

The gray image is a code over GF(2) with n=648, k=16 and d=272.
This code was found by Heurico 1.16 in 69.3 seconds.