The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+76x^40+64x^41+192x^42+262x^43+593x^44+1048x^45+2800x^46+4730x^47+7537x^48+10264x^49+10422x^50+10300x^51+7540x^52+4760x^53+2741x^54+1028x^55+579x^56+232x^57+188x^58+62x^59+49x^60+16x^61+34x^62+2x^63+6x^64+6x^66+2x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=400, k=16 and d=160.
This code was found by Heurico 1.16 in 35.9 seconds.