The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+182x^39+781x^40+1416x^41+2160x^42+2538x^43+2651x^44+2372x^45+1907x^46+1278x^47+667x^48+236x^49+118x^50+34x^51+27x^52+8x^53+7x^54+1x^56

The gray image is a code over GF(2) with n=352, k=14 and d=156.
This code was found by Heurico 1.16 in 1.56 seconds.