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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  1  2  2  2
 0 12  0  4  0  0  4  4  8  8  4 12  8 12  0 12  4  8  4  0 12 12  0  0 12 12  0  8  8  0 12 12  0  8  8  0  0  8  8 12 12  4  0 12 12  0  0  8  4  8  4  4  0
 0  0 12  4  0 12 12  0  8  4  4  0 12  4  0  8  8 12 12  8 12  0  0 12 12  4  0  0  4 12  8  8  0  4  8 12  8 12  0  0  8  8  4  0 12 12  4 12 12  0 12 12 12
 0  0  0  8  0  0  8  0  0  8  0  0  8  0  8  8  0  0  0  8  8  8  0  0  0  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  8  8
 0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  8  8  8  8  0  8  8  0  8  8  0  0  8  0  8  0  0  8  8  0  0  8  0  8  0  0  8  0  0  0  0  8  0  0  8  8
 0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  8  8  0  8  0  8  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+158x^48+16x^49+20x^50+96x^51+80x^52+1312x^53+40x^54+96x^55+148x^56+16x^57+4x^58+56x^60+4x^64+1x^96

The gray image is a code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 14.9 seconds.