The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^39+226x^40+176x^41+480x^42+152x^43+477x^44+144x^45+208x^46+80x^47+12x^48+8x^51+3x^52+1x^56

The gray image is a code over GF(2) with n=344, k=11 and d=156.
This code was found by Heurico 1.16 in 0.0669 seconds.