The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+55x^46+182x^47+351x^48+766x^49+1249x^50+1884x^51+2511x^52+2558x^53+2416x^54+1916x^55+1213x^56+720x^57+280x^58+102x^59+69x^60+38x^61+21x^62+10x^63+15x^64+14x^65+7x^66+2x^67+4x^70

The gray image is a code over GF(2) with n=424, k=14 and d=184.
This code was found by Heurico 1.16 in 2.91 seconds.