The generator matrix

 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  1  8  1  1  1  1  1  1  1  0  1  2  1  2  4  1  1  2  1  1  1  8  1  1  1  2  1
 0  2  0  6  4  6 12  2  0  6  8 14  4  4  2 10  8  2  6  4  6  6 10  4 12  4  2  2 14  2 12  8 12  8 12  2  2 10  6  6  2 10  2 14 14  6  4  2 10 10  6  0  8
 0  0 12  0  4  0  8  0  4  4  0  4  4  0 12 12  8  4  8  4  4 12  0 12  8  0  4 12  0  8  8  0 12  4 12  8  8  4 12  0 12  0  8 12  0  8  8  0  4  4  4  4  0
 0  0  0 12  0  8  8  4  4  4  4  0 12  4  0  4 12  0  8  8  4  4  4 12  0  0  4  8  4  0  4  0  8  4  8  0 12 12  0  0  8  8  4  8  0  8 12 12 12  4 12 12  0
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  0  0  8  0  8  0  0  0  8  0  0  8  8  0  8  8  0  8  8  8  8  0  8  8  0  8  0  8  0  0  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+278x^48+24x^49+294x^50+384x^51+782x^52+720x^53+630x^54+384x^55+357x^56+24x^57+130x^58+62x^60+2x^62+19x^64+4x^68+1x^88

The gray image is a code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 5 seconds.