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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+216x^49+102x^50+210x^51+292x^52+442x^53+274x^54+204x^55+84x^56+196x^57+7x^58+2x^59+6x^60+10x^61+1x^66+1x^88

The gray image is a code over GF(2) with n=424, k=11 and d=196.
This code was found by Heurico 1.16 in 97.4 seconds.