I have studied behavioral psychology (of course, I'm no expert) and yet I have still seen no definitive evidence of moral codes among animals. What I have seen is patterns of behavior due at least in part to social stresses, which is not the same thing. What have you studied that has lead you to believe otherwise? There are alternative forms of evidence that you could provide other than a picture.
Also, not all cultures developed moral stigmas about killing and sex, and even the ones that have moral guidelines regarding these things differ drastically from each other. The Romans and the Greeks had very few social restrictions when it came to sex, and most early meso-american cultures were not against killing for virtually any reason.
As far as your comment about Moses is concerned; religion existed long before Moses; among the Jews and otherwise. I think you would be hard pressed to come up with an example of a moral code that predated religion, as it is near impossible to tell when the advent of religion came about.