I think there is a difference between a sense of morality and a code of morality but there is a lot of overlap because the latter comes from the former and in turn the latter helps to refine and communicate the former.
Codes make it easier to work with a sense, especially in a social setting, as they aid the communication of the sense. Some famous examples of codes would be Bushido, the Ten Commandments, the Code of Chivalry and the Geneva Conventions.
Generally that is what a code of morality is, the articulation of a sense of morality. In turn the articulation can help develop the sense and so there is a feedback relationship between the two.
People do not necessarily need a code like the Ten Commandments to avoid stealing or murdering. However it definitely helps to have that articulation when negotiating social contracts with your fellow humans.
In general one generates one’s sense of morality from a very complex ongoing computation of expectations about the behaviours of others. This computation is also factored with anticipations of what others would expect of one in reciprocation and what they may do in reprisal for contravention.
So for example one might generate the sense that a house guest should not just take a crap in their own pants to save himself the trouble of getting up to use the house toilet facilities, because the smell and mess would be unpleasant for all in company. In turn one would calculate that one probably should not do that oneself for fear of being ostracised in reprisal.
It is from these kinds of calculations that all the social pillars of human civilisation are piled up. Example social pillars would be the practices of trade and concepts of property.
Some of these basic expectations are hard wired and quite inflexible. Probably most are calculated on-the-fly so to speak and can be very dynamic.
Ultimately all these calculations are in the service of the survival imperative. This is because they practically help one survive and prosper. However because there are innumerable solutions to the survival problem there can be very different valid moral calculations depending on the circumstances.
A rabbit has a physiology and behaviour adapted to solve the survival problem in particular ways. Consequently for the rabbit natural solutions like “it is good to be quick to runaway from danger”, “it is bad to be far from a bolt hole” come up often and sharply.
For the lion’s situation those calculations do not come up much, instead they tend to get things like “sneaky is better than fast”, “watch out for big animals with horns”, “target the slow ones in a crowd of prey”, “only the fierce get the bitches”. These are calculations which better fit the lion’s way of being.
Codes of morality are more or less articulations of these kinds of calculations. Some of these codes of course are asserted to come from a negotiation with a non-human intelligence as with the aforementioned Ten Commandments which is said to be part of deal made with a creator god called Jehovah or something like that.
Assuming that is true that in no way invalidates the basis of that code because there really is no particular reason why a moral negotiation need be wholly intra-species unless one is a massively bigoted species chauvinist like the humanists claim to be.