The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+52x^31+116x^32+186x^33+465x^34+684x^35+2141x^36+3556x^37+8812x^38+9814x^39+13831x^40+9914x^41+8750x^42+3590x^43+2224x^44+638x^45+386x^46+190x^47+106x^48+36x^49+15x^50+6x^51+11x^52+6x^53+2x^54+1x^56+2x^58+1x^64

The gray image is a code over GF(2) with n=320, k=16 and d=124.
This code was found by Heurico 1.16 in 26.4 seconds.