The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^44+146x^45+438x^46+722x^47+773x^48+1322x^49+1373x^50+1316x^51+766x^52+698x^53+416x^54+132x^55+19x^56+6x^57+5x^58+4x^59+3x^60+4x^61+5x^62+2x^63+3x^64+2x^66+1x^68+1x^70

The gray image is a code over GF(2) with n=400, k=13 and d=176.
This code was found by Heurico 1.16 in 0.686 seconds.