The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+37x^38+292x^39+301x^40+862x^41+668x^42+1440x^43+1122x^44+1472x^45+623x^46+748x^47+223x^48+222x^49+70x^50+56x^51+16x^52+20x^53+10x^54+8x^55+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 0.843 seconds.