Now what I just typed was complete randomness. In this can you find any deciferable piece of information. No. Compared to this example that shows order:
Your analogy isn't adequate because if enclosed in the right markers
any pattern of the DNA is "meaningful" -- guessing at what you might mean. That is, it produces a protein through the transcription mechanism.
Now some proteins might not be good for much and some will be. Is it the "good for something" that you mean by "meaningful". Some are.
Duplicating an entire sequence might produce twice as much of an existing protein -- this has effects on the organism (some of the time). Some of those effects maybe harmful, some neutral and some maybe beneficial. Is beneficial what you mean by "meaningful"? Some are.
Those which are actually harmful will be weeded out by selection. Leaving us with a increase in "meaningful" "information".
Remember, the DNA code is
not a language in which only some orders of letters produce real output.
Any order within the gene produces real output.