The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^51+152x^52+226x^53+484x^54+1058x^55+1877x^56+3136x^57+4879x^58+7008x^59+9053x^60+9678x^61+8858x^62+7304x^63+5194x^64+3100x^65+1561x^66+872x^67+499x^68+198x^69+131x^70+78x^71+44x^72+44x^73+20x^74+8x^75+12x^76+2x^77+3x^78

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 49.5 seconds.