The generator matrix

 1  0  0  1  1  1 10 14 14  4  1  1  1  1  1  4 10  1  6  1  1  1  1  4 10  0  8  1  8  8  1  1  1  1 14  1  1  1  1  1 12  1  4  1
 0  1  0  0  5  5  1 14  1  1  1 14 12  9 10 14  1 11  1  7 14  7  8  1  4  2 12 14  1  1 13  5 11  0  6  6  8  8  4  1  2 15  1  4
 0  0  1  3 11  8  7  1  2  7 10  7  6  9  9  1  9  1  0 10 12 15  5  1  1  1  1  2  0 10  4  1  0 12  1  5 13  7  7 11  1  8 10 10
 0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  0  8  8  8  8  8  0  8  8  0  8  8  8  8  0  8  8  0  8  0  0  0  0  8  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+329x^40+828x^41+1208x^42+1244x^43+1459x^44+984x^45+936x^46+616x^47+324x^48+140x^49+80x^50+28x^51+13x^52+2x^56

The gray image is a code over GF(2) with n=352, k=13 and d=160.
This code was found by Heurico 1.16 in 0.453 seconds.