The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1 10  1  1  1 12  1  1  1  1  8  1  6  4  1  1 10  1  1  1  6  1  1  1 14  1 10  1  4  1 14  1  1  1  1 14  0  0  1  4  6 14  1  8  1  1  1  1  1  0
 0  1 11  6  1  1  0 11  1  6  1 13  1  0  3  5  1  6 12 15  1  1  2  1  1  7 12  1  9  4  6  1 13  9  7  1  3  1  3  1  8  1  2  4 15 12  1  1  1 13  1  1  1  4  1  4 13  6  5  0  1
 0  0 12  0  0  0  0  0  0  8  8  4  0  4  0  8  8  4  4  4  4  4  4  4  0  0  8  4 12  8  8  4 12  8  4 12  0  0  0  4  4  4  8  8  4  4  0 12  0  8  0 12  0  4  8 12 12  4  8 12  4
 0  0  0 12  0  0 12  8  4  8 12  0  8  0  4 12  0  0  0 12  0 12  4  8 12  8  0  0 12 12 12 12  4 12 12  8  4  4 12  8  4  4  0  0  8  0  4  0  8  0  4  0  8  0  8 12 12  4 12 12  4
 0  0  0  0  4  0  0 12  8  0  8  0  0  4  4 12  8 12  4  0  8 12  4 12  8 12  8 12  8  8  4  8 12  0  4  8  0 12 12  0  4 12  4 12  4  0  4  4  4  4  8  8  8  8  4  4 12  8 12  0  0
 0  0  0  0  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  8  0  8  8  0  0  8  8  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0  0  8  8  8  8  0  8  8  8  8  0  0  8  8  8
 0  0  0  0  0  0  8  8  0  8  8  8  8  0  0  8  8  0  8  8  8  0  8  0  8  0  0  0  0  0  0  0  8  0  0  8  0  8  8  0  8  8  0  8  8  0  0  8  8  8  8  0  0  0  0  0  0  8  0  8  0

generates a code of length 61 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+52x^51+123x^52+208x^53+379x^54+820x^55+1514x^56+2944x^57+4839x^58+6896x^59+9589x^60+11010x^61+9519x^62+6888x^63+4815x^64+2902x^65+1478x^66+748x^67+351x^68+178x^69+85x^70+68x^71+46x^72+34x^73+19x^74+16x^75+7x^76+4x^77+1x^78+2x^84

The gray image is a code over GF(2) with n=488, k=16 and d=204.
This code was found by Heurico 1.16 in 48.9 seconds.