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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+74x^49+152x^50+182x^51+416x^52+350x^53+612x^54+604x^55+603x^56+398x^57+350x^58+78x^59+119x^60+68x^61+32x^62+28x^63+12x^64+4x^65+6x^66+2x^69+4x^71+1x^84

The gray image is a code over GF(2) with n=440, k=12 and d=196.
This code was found by Heurico 1.16 in 0.439 seconds.