The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+128x^39+387x^40+592x^41+992x^42+1328x^43+1394x^44+1328x^45+992x^46+592x^47+279x^48+128x^49+37x^52+13x^56+1x^68

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 16.8 seconds.