The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  2  0 12  1  4  2  1  1 12  1  8  1  8  1  1  8  1  8  1  1  2 12  2  1
 0  2  0  2  0  0  2  6  4 10  4  6 10 14  4  2  2  2  4  8  6  0  0  2 12  2 10 12  2 12  2  2  8 14  2  4  0
 0  0  2  2  0  6  2  4  0  2  2  0 10 12  2 10  6  0  6 10 12  2  6  4 12  0  6  4  8 10  2 14  0 12 14  2  0
 0  0  0  4  0  0  0  0  0  0  8 12  4 12  8  0 12 12  4  4  4 12 12  8  4  0  8 12 12  8 12 12  8  4  0 12  0
 0  0  0  0 12  0  0  0  0  0 12  8 12 12  4 12 12  0 12  8 12  8  4  0  0  8  8 12 12 12  0  4  8  4  4  8  0
 0  0  0  0  0 12  8 12  4 12  4  4  4  0  8  8  0  0  4  0  0  4 12  8  0 12 12  4  0  8  4  4 12  0  4 12  0

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

Homogenous weight enumerator: w(x)=1x^0+62x^28+186x^29+345x^30+804x^31+1353x^32+2468x^33+4389x^34+7340x^35+10316x^36+11066x^37+10054x^38+7488x^39+4610x^40+2562x^41+1186x^42+652x^43+340x^44+156x^45+89x^46+36x^47+20x^48+10x^49+1x^50+2x^52

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 33.8 seconds.