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

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

Homogenous weight enumerator: w(x)=1x^0+76x^57+319x^58+620x^59+1115x^60+1466x^61+2387x^62+3264x^63+5256x^64+6352x^65+7726x^66+8238x^67+8050x^68+6358x^69+5196x^70+3336x^71+2403x^72+1334x^73+924x^74+492x^75+301x^76+140x^77+84x^78+48x^79+24x^80+14x^81+3x^82+2x^83+1x^84+4x^85+1x^86+1x^92

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 72.1 seconds.