The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  2  2
 0 12  0  4  0  0  4 12  0  0  4 12  0  0  4 12  8  8  8  8 12  4  8  8 12  4  8  8 12  4  8  8 12  4  0  0  4  4 12  0  0 12  4  4
 0  0 12  4  0 12  4  0  8  4 12  8  8  4 12  8  4  4  8  4 12  8  8  4 12  8  0 12  4  0  0 12  4  0  0 12  4 12 12 12  8  0 12  0
 0  0  0  8  8  8  0  8  8  8  8  8  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  8  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+96x^42+331x^44+72x^46+3x^48+8x^50+1x^76

The gray image is a code over GF(2) with n=352, k=9 and d=168.
This code was found by Heurico 1.16 in 0.189 seconds.