The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+122x^39+155x^40+264x^41+232x^42+566x^43+263x^44+208x^45+79x^46+74x^47+28x^48+40x^49+6x^50+2x^51+1x^52+1x^54+4x^55+1x^58+1x^66

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 61.5 seconds.