The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+58x^28+92x^29+304x^30+568x^31+1080x^32+2458x^33+4235x^34+7492x^35+10679x^36+11480x^37+10743x^38+7620x^39+4283x^40+2484x^41+1029x^42+428x^43+266x^44+124x^45+69x^46+20x^47+16x^48+2x^49+4x^50+1x^60

The gray image is a code over GF(2) with n=296, k=16 and d=112.
This code was found by Heurico 1.16 in 23.4 seconds.