The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+162x^40+16x^41+346x^42+240x^43+599x^44+240x^45+260x^46+16x^47+111x^48+34x^50+20x^52+2x^56+1x^76

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 0.138 seconds.