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

generates a code of length 67 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+40x^57+298x^58+588x^59+971x^60+1618x^61+2311x^62+3278x^63+4852x^64+6668x^65+8060x^66+8374x^67+7834x^68+6732x^69+4968x^70+3468x^71+2177x^72+1296x^73+926x^74+532x^75+275x^76+114x^77+69x^78+46x^79+13x^80+12x^81+8x^82+2x^83+4x^84+1x^88

The gray image is a code over GF(2) with n=536, k=16 and d=228.
This code was found by Heurico 1.16 in 72.9 seconds.