The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+459x^40+96x^41+676x^42+416x^43+974x^44+416x^45+536x^46+96x^47+250x^48+132x^50+42x^52+1x^56+1x^64

The gray image is a code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 25 seconds.