The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+447x^40+80x^41+592x^42+432x^43+1102x^44+432x^45+528x^46+80x^47+271x^48+96x^50+34x^52+1x^72

The gray image is a code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 50.2 seconds.