The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^46+88x^47+348x^48+224x^49+800x^50+682x^51+1349x^52+1128x^53+1368x^54+688x^55+762x^56+152x^57+280x^58+68x^59+82x^60+24x^61+30x^62+8x^63+16x^64+8x^65+2x^67+1x^68+1x^80

The gray image is a code over GF(2) with n=424, k=13 and d=184.
This code was found by Heurico 1.16 in 1.17 seconds.