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

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

Homogenous weight enumerator: w(x)=1x^0+226x^44+244x^45+924x^46+840x^47+1963x^48+2800x^49+4864x^50+6456x^51+9345x^52+9888x^53+9656x^54+6756x^55+4915x^56+2688x^57+1774x^58+820x^59+812x^60+188x^61+226x^62+36x^63+72x^64+26x^66+4x^67+9x^68+2x^70+1x^72

The gray image is a code over GF(2) with n=424, k=16 and d=176.
This code was found by Heurico 1.16 in 57.8 seconds.