The generator matrix

 1  0  1  1  1 14  1  1  0 14  1  1  1  1  2  1  1  8  0  1  1  1  6  1  1  1 10  1  1 14 12 12  1  1  1  8  1 14  0  4  1  1  1  1  1  2  1  2  1  1
 0  1 11  6  1  1  8  3  1  1 14  9  6 13  1 15  4  1  1  6 11  1  1  0 13  0  1 14  3  1  1  1  5  0 15  1  7  1  1  1  2  3  3  3  0  1  1 12  4 14
 0  0 12  0  0  0  0  8 12  4  4  4 12  0 12  0  8  4  8  0  8 12  0 12  8  0  0  4  8  4 12  0  8 12 12  4  8  4  0 12  0 12  4 12  8  4  4  4  4  4
 0  0  0 12  0  0  8  8  8  8  0  8  8  8  8  0  0 12  4 12  4 12  4 12  4  4 12 12  4  4 12  8  8  4  8  8  8  4  0  4  8  8  0  4  4  0 12  8  8  4
 0  0  0  0  4 12 12  8  4  0  0  4  4  4  0  8  4  4  0  4  0  4  4  8  4 12  4 12  4  4  8  0  8  8  4  0 12 12 12  4 12 12  0 12  8  4  0  4 12  4

generates a code of length 50 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+184x^44+272x^45+840x^46+1200x^47+2005x^48+2352x^49+2782x^50+2400x^51+1933x^52+1200x^53+742x^54+240x^55+114x^56+16x^57+42x^58+42x^60+10x^62+8x^64+1x^68

The gray image is a code over GF(2) with n=400, k=14 and d=176.
This code was found by Heurico 1.16 in 4.52 seconds.