The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+296x^48+200x^49+987x^50+808x^51+1327x^52+1040x^53+1326x^54+848x^55+868x^56+168x^57+236x^58+8x^59+45x^60+10x^62+14x^64+1x^66+8x^68+1x^72

The gray image is a code over GF(2) with n=424, k=13 and d=192.
This code was found by Heurico 1.16 in 20.7 seconds.