Nurbspath to follow terrain via schrinkwrap deform issue

Dear all,

I have heightmap which I want to use to layout a road following the exact hills.
I loaded this into blender and generated the terrain which went ok, then I made a path for the road I want to make to follow the landscape using the schrinkwrap modifier.

However something strange happens to my Nurbsparth after applying schrinkwrap is that my path looks like it goes in all directions and it does not follow the path I layed out above into the terrain.

Instead it became a zigzag path as you can see in the image in the think black line on the land:

I tried the apply on spline function, which smoothens the line, but still is not exact where i drawout the line, causing the road to go "into"the land with this function instead of being at the exact surface.

Any tips on how to solve this and get the path smooth into the terrain where my path is set out? Are my settings wrong or what do I do wrong?

Thanks in advance.