The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^39+490x^40+564x^41+1162x^42+1050x^43+1621x^44+1054x^45+1158x^46+464x^47+337x^48+70x^49+58x^50+38x^51+30x^52+6x^53+6x^54+2x^57+1x^60

The gray image is a code over GF(2) with n=352, k=13 and d=156.
This code was found by Heurico 1.16 in 0.596 seconds.