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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+143x^44+4x^45+415x^46+40x^47+624x^48+320x^49+1337x^50+1496x^51+2533x^52+2424x^53+2899x^54+1496x^55+1177x^56+320x^57+535x^58+40x^59+324x^60+4x^61+170x^62+49x^64+20x^66+12x^68+1x^80

The gray image is a code over GF(2) with n=424, k=14 and d=176.
This code was found by Heurico 1.16 in 5.83 seconds.