The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+20x^41+76x^42+136x^43+286x^44+586x^45+1285x^46+2480x^47+3544x^48+5496x^49+5009x^50+5492x^51+3565x^52+2476x^53+1239x^54+556x^55+252x^56+116x^57+54x^58+36x^59+28x^60+10x^61+11x^62+4x^63+3x^64+5x^66+1x^68+1x^70

The gray image is a code over GF(2) with n=400, k=15 and d=164.
This code was found by Heurico 1.16 in 9.68 seconds.