The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+72x^40+200x^41+227x^42+392x^43+304x^44+360x^45+216x^46+184x^47+69x^48+16x^49+2x^50+2x^56+3x^58

The gray image is a code over GF(2) with n=352, k=11 and d=160.
This code was found by Heurico 1.16 in 0.0645 seconds.