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

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

Homogenous weight enumerator: w(x)=1x^0+80x^49+196x^50+346x^51+317x^52+396x^53+210x^54+220x^55+101x^56+68x^57+44x^58+22x^59+20x^60+16x^61+6x^62+4x^63+1x^84

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 0.194 seconds.