Your general impression on looking at the body, is that there simply is no way that this person committed suicide.
Whilst it looks like the weapon used in this case was a gun, instead of the back of the skull being blown out, it is the front. The entry would lies in the centre of the back of her neck.
There is bruising around the neck and wrists, though you're not exactly an expert in this, so you can't tell if it happened before or after death.