The generator matrix

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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+58x^53+230x^54+586x^55+998x^56+1988x^57+2159x^58+3752x^59+4342x^60+5160x^61+3566x^62+3938x^63+2363x^64+1820x^65+896x^66+400x^67+208x^68+178x^69+48x^70+26x^71+22x^72+8x^73+9x^74+2x^76+4x^77+4x^78+2x^79

The gray image is a code over GF(2) with n=488, k=15 and d=212.
This code was found by Heurico 1.16 in 12.1 seconds.