The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+107x^44+68x^45+346x^46+292x^47+944x^48+828x^49+1860x^50+2420x^51+2880x^52+2332x^53+1766x^54+876x^55+820x^56+292x^57+264x^58+60x^59+148x^60+46x^62+27x^64+4x^66+2x^70+1x^76

The gray image is a code over GF(2) with n=416, k=14 and d=176.
This code was found by Heurico 1.16 in 4.45 seconds.