The generator matrix

 1  0  1  1  1 14  1  1 12  1  1  2  1  1  8  1  1 14  1  1  0  1  1 12  2  0  6 14  4 12 10  2 12  1  1  1  1  6  1  1  2  1  1  6  2  6 14  1  2  8  1  1  2  1  4
 0  1 11 14  5  1  7 12  1  2  9  1  8  3  1  6 13  1  4 15  1 10  1  1  1  1  1  1  1  1  1  1  2  0  0 14  2  1  4  4  1 14  2  1  1  1  1  6  2  1 13  2 12  1  1
 0  0 12  4  8 12 12  0  0  4  8 12  4  8 12  0 12  4  4  8  0  0 12  0  4 12  0  8  4  4  0  8  8  0  4  4  0 12 12  8 12  8 12  4  4  0  8  0  4  4  8  8  4  0  4
 0  0  0  8  0  8  8  8  8  0  8  0  0  8  0  0  0  8  8  0  8  8  8  0  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  0  8  8  8  0  8  8  8  8  8  8  8  8  8  8  0

generates a code of length 55 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+389x^52+184x^53+448x^54+168x^55+345x^56+136x^57+256x^58+24x^59+89x^60+2x^64+5x^68+1x^84

The gray image is a code over GF(2) with n=440, k=11 and d=208.
This code was found by Heurico 1.16 in 2.37 seconds.