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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+14x^57+156x^58+320x^59+543x^60+864x^61+1796x^62+1990x^63+3581x^64+4498x^65+6892x^66+7690x^67+8917x^68+7662x^69+6830x^70+4660x^71+3845x^72+1896x^73+1510x^74+732x^75+503x^76+258x^77+142x^78+86x^79+66x^80+32x^81+18x^82+10x^83+13x^84+8x^85+3x^88

The gray image is a code over GF(2) with n=544, k=16 and d=228.
This code was found by Heurico 1.16 in 99.8 seconds.