The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+380x^42+260x^44+380x^46+1x^56+2x^60

The gray image is a code over GF(2) with n=352, k=10 and d=168.
This code was found by Heurico 1.16 in 0.0777 seconds.