The generator matrix

 1  0  1  1  1 14  1  2  1 12  1  1  1  1  8  1  1  4  1  1  1  1  0  0  6 10  6 10  0  4  2  6  1  1  1  2  1  6  6  1  1 12  4  2
 0  1 11  6 13  1 12  1  7  1 14  5  8  3  1  2  9  1  4  1 10 15  1  1  1  1  1  1  1  1  4  1 15 10  5  1 11  1  1  1  8  1  1  4
 0  0 12  0  4  4  8  4  4  8  4  0 12  8 12  4  0 12 12 12  8  8  0  8  0  0  0  0 12  4 12  8  0  8  0  4 12  8 12 12  0  8  0 12
 0  0  0  8  0  8  8  8  8  0  0  8  0  8  0  8  0  0  8  8  0  0  8  8  0  8  0  8  8  8  0  0  8  8  0  0  8  8  0  8  0  0  8  0
 0  0  0  0  8  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  0  0  8  8  8  0  0  0  0  8  8  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+223x^40+348x^41+572x^42+564x^43+768x^44+536x^45+528x^46+328x^47+171x^48+12x^49+20x^50+4x^51+11x^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 0.311 seconds.