The generator matrix

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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+16x^45+81x^46+68x^47+138x^48+300x^49+288x^50+604x^51+1311x^52+1544x^53+2837x^54+2128x^55+2808x^56+1472x^57+1260x^58+704x^59+280x^60+232x^61+104x^62+76x^63+49x^64+20x^65+24x^66+4x^67+15x^68+9x^70+4x^72+4x^74+2x^76+1x^78

The gray image is a code over GF(2) with n=440, k=14 and d=180.
This code was found by Heurico 1.16 in 33.8 seconds.