No, not all codified constitutions are entrenched.
People say that Britain's constitution is uncodified, but there are parts that are codified. The Human Rights Act 1998 is an example of one part of Britain's constitution that is codified. However, it is not entrenched, and as it does not apply to Westminster, Parliament could simply pass a statute that overruled it.
Normally constitutions that are completely codified though, like America's, are entrenched.