Let's get some things straightened out here. For starters, animals have no moral code. Most animals lack the cognitive ability to perform any higher intellectual function, let alone grasp abstract concepts. In fact, most creatures in the animal kingdom don't even think, per se - they react to external stimuli, which is different. You're focusing a little bit too much on advanced vertebrates there. Secondly, even atheists follow some form of a philosophy in life, and to simplify matters for the sake of this discussion, we'll treat religion as a philosophy with an added aspect of divinity. There are people who believe in the divine and there are people who don't, however both groups *have beliefs*, and it's their belief systems that help them co strict moral hierarchies. Even the biggest nihilist believes in something, it's an integral part of the human existence and one of many things that differentiate us from animals.
As Paul Stanley likes to say: we're all animals!
Primatologists have found behaviors in apes that suggest otherwise. They have been shown to exhibit signs of guilt which is a huge indicator of morals.