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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+140x^47+254x^48+682x^49+448x^50+1062x^51+864x^52+1516x^53+845x^54+972x^55+420x^56+480x^57+168x^58+184x^59+48x^60+68x^61+10x^62+8x^63+13x^64+6x^65+2x^67+1x^70

The gray image is a code over GF(2) with n=424, k=13 and d=188.
This code was found by Heurico 1.16 in 1.08 seconds.