The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+189x^38+160x^39+278x^40+608x^41+985x^42+1280x^43+1258x^44+1280x^45+952x^46+608x^47+232x^48+160x^49+152x^50+14x^52+19x^54+8x^56+7x^58+1x^64

The gray image is a code over GF(2) with n=352, k=13 and d=152.
This code was found by Heurico 1.16 in 33.5 seconds.