The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+55x^34+146x^35+244x^36+490x^37+723x^38+1178x^39+2274x^40+3622x^41+4897x^42+5502x^43+4951x^44+3666x^45+2221x^46+1206x^47+708x^48+386x^49+212x^50+152x^51+73x^52+28x^53+20x^54+8x^55+5x^56

The gray image is a code over GF(2) with n=344, k=15 and d=136.
This code was found by Heurico 1.16 in 12.7 seconds.