The argument that God(pick a God, any God, is the source of a moral code, is a simple appeal to authority. It reduces social responsibility to the universal parental, "Because I said so." A parent knows a toddler lacks the mental wherewithal to process moral philosophy, so "Because I said so," is sufficient information, at least for the moment. The ultimate question of life, the universe, and everything turns out to be, "Why should I?" and "Because I said so," falls so very short of an answer for real problems.
After we've picked our God(let's make it a well documented one, just because it's easier) I think we can easily demonstrate there is nothing objective about the established rules. Certainly not when it comes to stoning people for various sins.
The problem of a moral code is always in the fine print. We all understand that it is wrong to kill someone, in the general sense, but as soon as we get to specifics, it gets complicated. It turns out, no matter how sacred life may be, as a concept, there's a hundred exceptions about when it's perfectly okay to smash someone's skull. God won't mind one bit.
Even when we can all(mostly all) agree on something, times change and our old rule doesn't work as it once did. It turns out, the list of people who can be stoned to death, gets shorter every millennium, or so.
The bullet points of any moral code, for any culture or society are pretty easy to understand. It's the footnotes that get complicated.
