The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+492x^38+1192x^39+2994x^40+4948x^41+7809x^42+9660x^43+11226x^44+9984x^45+7939x^46+4784x^47+2769x^48+1060x^49+471x^50+108x^51+58x^52+8x^53+25x^54+8x^56

The gray image is a code over GF(2) with n=352, k=16 and d=152.
This code was found by Heurico 1.16 in 67.5 seconds.