Not really. Even the comparison of transcription to an interpreter is pretty flaky - although the whole transcription process could be considered interpretation.
I graduated in Human Biology and spend around 12 years doing environmental physiology research and development before switching track to a career in software development, from assembler code, through C and C++, to Java. I'm retired now, but I keep up to date.
So you see I'm reasonably well qualified to say that DNA isn't really like computer code. It's an easy comparison to make because it's the closest analogy we have, but it's just an analogy.
It's easy and tempting to look at something complex or that's not understood and claim agency and purpose - and we seem primed to do that, but there are no well-defined criteria to make that judgement, and every time we've investigated such situations, we've discovered that the more we understand them the more they look natural and the less they look artificial. Labelling it as intelligent design is a dead-end non-explanation - it tells you nothing about the phenomenon you're trying to understand, and introduces a new entity for which there is no evidence or explanation - it raises more questions and answers none.
By continuing to investigate the origins of life, we've made a lot of new and remarkable discoveries - how cell membranes can spontaneously self-assemble, grow, and divide, how simple metabolic cycles can spontaneously arise, how RNA can act as both a template and an enzyme, and so-on. We don't yet know how DNA originated, but we're making progress.
Intelligence can construct ordered systems, but so can nature; complexity is an emergent property of low entropy systems with significant amounts of free energy. All of chemistry can be seen as the interactions between elements of a coded system where the electrons in the outer shell are instructional.
Well that's debatable - the earliest replicators (just a molecule that can duplicate itself or be duplicated) would probably not qualify for most definitions of 'life'; the first proto-cells likewise - they'd just swell and divide, splitting their contents. The major complexities would develop - evolve - over time.
There's always information.
A simple replicator doesn't even grow, it just makes copies or gets duplicated. As long as the duplication process is imperfect, it will evolve.
If you like. but everything can be considered to have and so encode information. Life is a particularly complex and indirect way of increasing entropy through oxidation; as
Albert Szent-Györgyi said, "
Life is nothing but an electron looking for a place to rest".
That's true only for complex life where individual creatures develop according to an inherited template. Simple replicators can form competitive ecosystems with a variety of roles and niches, without individual development or growth - plenty of time for that to develop later.
