The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^44+36x^45+352x^46+272x^47+889x^48+1344x^49+1348x^50+2944x^51+1759x^52+2968x^53+1378x^54+1360x^55+766x^56+256x^57+338x^58+32x^59+110x^60+4x^61+38x^62+30x^64+2x^66+5x^68+2x^72

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 5.06 seconds.