The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+228x^39+903x^40+1162x^41+1506x^42+1222x^43+1135x^44+796x^45+653x^46+290x^47+184x^48+72x^49+32x^50+4x^51+1x^52+2x^53+1x^54

The gray image is a code over GF(2) with n=344, k=13 and d=156.
This code was found by Heurico 1.16 in 0.438 seconds.