The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+403x^48+128x^49+672x^50+384x^51+944x^52+384x^53+672x^54+128x^55+362x^56+8x^60+8x^64+2x^80

The gray image is a code over GF(2) with n=416, k=12 and d=192.
This code was found by Heurico 1.16 in 13.1 seconds.