The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+102x^35+534x^36+954x^37+1877x^38+3076x^39+4819x^40+6826x^41+9057x^42+10744x^43+9341x^44+7210x^45+4851x^46+2792x^47+1704x^48+848x^49+499x^50+180x^51+81x^52+32x^53+4x^54+2x^57+2x^59

The gray image is a code over GF(2) with n=344, k=16 and d=140.
This code was found by Heurico 1.16 in 39.7 seconds.