The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+78x^39+462x^40+596x^41+1315x^42+898x^43+1525x^44+1084x^45+1242x^46+412x^47+351x^48+92x^49+73x^50+34x^51+21x^52+4x^53+1x^54+2x^55+1x^62

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 0.578 seconds.