The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  8  1  1 10  1  1  2  4  1  1  1  4  1  1  8  1 12  1  1  8  1  1  2  1  2  1  0  1  2  1  1  4  2  1  1
 0  1 11  6  5  1 11  0  1  5  1  6 13  1  8  1  3  6  1  1  4  1  1 10  1 15  1  8 14  1 13  1  3  2  1  5  0 10 11  6  7  1  2  8 14  4  8  8  8  0
 0  0 12  0  0  0  0  4  4 12 12  0  8  8  8  0  8  4  4  4  4  0  4  8  8 12  0  4  4  4  8  4  4  8  4  0 12  4  0 12  8  4  0  4  4  4  0  0  0  0
 0  0  0 12  0  4  4  4 12 12  8  0  4  8  4  4  0  4 12  8  8  4  8  0 12  4  4  0  0  8  4  4 12  4  0  8  4  4 12  0  4  4  4  8  0  0  4 12  4  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  8  0  0  0  0  0  8  8  8  0  8  8  8  0  8  8  8  8  8  8  8  0  8  0  0  8  0  0  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  0  8  8  0  8  0  0  0  8  8  0  0  8  8  0  0  8  0  8  8  0  0  8  0  8  0  8  0  0  0  8  0  8  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  8  0  0  8  0  8  8  8  8  8  0  0  0  0  0  8  0  0  8  0  0  0  8  0  8  8  0  8  8  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+72x^40+94x^41+241x^42+306x^43+1014x^44+948x^45+3627x^46+3924x^47+8327x^48+8076x^49+11888x^50+8006x^51+9216x^52+3918x^53+3241x^54+986x^55+1026x^56+252x^57+169x^58+80x^59+50x^60+22x^61+26x^62+10x^63+6x^64+2x^65+6x^66+1x^70+1x^78

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 36.3 seconds.