The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^40+434x^41+613x^42+718x^43+683x^44+546x^45+397x^46+314x^47+128x^48+88x^49+41x^50+8x^51+9x^52+4x^53+4x^54+1x^56+1x^62

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 0.221 seconds.