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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+121x^52+144x^53+515x^54+716x^55+1039x^56+2016x^57+1861x^58+4376x^59+2685x^60+5928x^61+2641x^62+4480x^63+1847x^64+2008x^65+932x^66+648x^67+381x^68+136x^69+167x^70+20x^71+57x^72+8x^73+23x^74+13x^76+5x^78

The gray image is a code over GF(2) with n=488, k=15 and d=208.
This code was found by Heurico 1.16 in 18.2 seconds.