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

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

Homogenous weight enumerator: w(x)=1x^0+67x^40+106x^42+623x^44+128x^45+36x^46+43x^48+18x^50+1x^52+1x^80

The gray image is a code over GF(2) with n=352, k=10 and d=160.
This code was found by Heurico 1.16 in 0.0663 seconds.