The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1 10  1  1 12  1  0  1  1  1  6  1  1  1  0  1  0  6  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  6  5  1 12 15  1 10  9  1  5  1  6  0  3  1 10  6  6  1  3  1  1  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  0  0  8  0  8  0  8  8  0  8  0  0  8  8  0  8  0  8  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  8  0  8  0  8  0  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  0  0  0  0  8  8  8  8  0  8  0  0  0  8  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  8  8  0  8  0  0  0  0  0  8  0  8  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  8  0  0  0  8  8  8  8  8  8  0  8  0  8  0  0  0  0  8  0  8  8  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  8  8  0  0  0  0  8  0  8  8  8  0  0  0  0  8  8  8  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  0  0  8  0  0  8  8  8  0  0  8  8  8  0  8  0  8  0  0  8  8  0

generates a code of length 40 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+49x^28+41x^30+18x^31+194x^32+90x^33+663x^34+592x^35+2112x^36+3264x^37+9986x^38+7300x^39+16916x^40+7300x^41+10008x^42+3264x^43+2081x^44+592x^45+701x^46+90x^47+135x^48+18x^49+79x^50+14x^52+24x^54+2x^56+2x^58

The gray image is a code over GF(2) with n=320, k=16 and d=112.
This code was found by Heurico 1.16 in 21.5 seconds.