The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+70x^45+200x^46+300x^47+375x^48+728x^49+1216x^50+1762x^51+2324x^52+2536x^53+2382x^54+1780x^55+1066x^56+660x^57+438x^58+220x^59+121x^60+86x^61+50x^62+24x^63+14x^64+12x^65+2x^66+10x^67+2x^68+4x^69+1x^76

The gray image is a code over GF(2) with n=424, k=14 and d=180.
This code was found by Heurico 1.16 in 6.43 seconds.