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

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

Homogenous weight enumerator: w(x)=1x^0+170x^44+76x^45+452x^46+436x^47+893x^48+1440x^49+2352x^50+3668x^51+4469x^52+5132x^53+4178x^54+3672x^55+2391x^56+1512x^57+870x^58+340x^59+374x^60+96x^61+122x^62+12x^63+80x^64+26x^66+3x^68+3x^72

The gray image is a code over GF(2) with n=424, k=15 and d=176.
This code was found by Heurico 1.16 in 17.1 seconds.