The Law of Moses surely was a moral code.
It was also a kind of photograph of what God is like.
Just like a photograph may represent a person but it is not that person. It may indicate what that person looks like.
The moral code of the law of Moses is not really what the believers in Jesus Christ live by directly. They live by the Spirit of Christ who is making His home in their hearts.
This living by Christ is also called living by the grace of Christ.
It is in contrast living by a moral code, even the best one written.
Paul even goes as far to say that we Christians are not under the law but under grace. Grace is so fine. Grace gets finer and finer. It penetrates down into the innermost motives.
It governs how a man in Christ reacts. It governs his reactions spontaneously. It is learned. And this learning to live by the Grace of Christ is a life long matter.
Now, here is where Paul the pioneer into the Christian life says that the believers are under grace rather than under the law.
"For sin will not lord it over you, for you are not under the law but under grace."
"But if you are led by the Spirit, you are not under the law."
Now a good question is "Where in the Gospels did Jesus teach anything like what Paul says here?"
In a post below I mention one very good place where Jesus teaches not being under the law but under grace.