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  2  1  1  1  1  1  1  1  1  1  1  1  1  4  1  1  2  1  1  1  1  1  4  1  4  2  2  1  1
 0 12  0  0  0  4 12 12  8  8  0  0  4  4  4 12  0  8  4  4  8  8  4  4  8 12 12 12 12  4  8  0  0 12 12  0 12  0  8  4  8 12  4  4  0  0  4 12  0  0  8  4  4  4 12
 0  0 12  0  4  4  4  0  8  0  4 12  4  4  0  8  0  8 12  8 12 12 12  8  0  8  8  4 12  0 12  4  8  4  4  4  0  0  0  8  0 12  8 12  8  8  0  4 12 12 12 12  4  0 12
 0  0  0 12  4  8  4  4  0  4  4  0  0 12  4  8  0 12  4  4 12  8  0  0 12  0  8  8  4  4  0 12  8  8 12  8 12  8 12  4  0 12  8  4 12  0  0 12  8 12  4  0  8  8  8
 0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  8  8  0  0  8  8  0  0  0  8  0  8  8  8  0  0  8  0  8  8  0  0  8  8  0  0  0  8  8  0  8  0  0  8  8  8  8  0  8

generates a code of length 55 over Z16 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+119x^50+8x^51+125x^52+144x^53+432x^54+464x^55+403x^56+144x^57+86x^58+8x^59+61x^60+24x^62+15x^64+11x^66+2x^68+1x^96

The gray image is a code over GF(2) with n=440, k=11 and d=200.
This code was found by Heurico 1.16 in 6.78 seconds.