The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+88x^41+44x^42+172x^43+421x^44+164x^45+44x^46+84x^47+1x^48+4x^49+1x^84

The gray image is a code over GF(2) with n=352, k=10 and d=164.
This code was found by Heurico 1.16 in 0.58 seconds.