The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+186x^40+336x^41+768x^42+432x^43+667x^44+432x^45+768x^46+336x^47+156x^48+4x^52+8x^56+1x^60+1x^64

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 2.04 seconds.