The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+23x^40+26x^42+64x^43+284x^44+64x^45+28x^46+11x^48+10x^50+1x^72

The gray image is a code over GF(2) with n=352, k=9 and d=160.
This code was found by Heurico 1.16 in 0.0345 seconds.