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

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

Homogenous weight enumerator: w(x)=1x^0+58x^49+45x^50+32x^51+85x^52+110x^53+394x^54+648x^55+392x^56+98x^57+61x^58+16x^59+26x^60+42x^61+6x^62+8x^63+6x^64+12x^65+5x^66+1x^68+1x^74+1x^96

The gray image is a code over GF(2) with n=440, k=11 and d=196.
This code was found by Heurico 1.16 in 35.2 seconds.