DNA is double-stranded so that it can replicate (forgive me ascribing motivation to chemistry), not so it can store extra information. It doesn't actually allow you to store any extra information at all, since each pair of nucleotides is uniquely determined. However, because the pairs are uniquely determined it means that you can split a single strand of DNA into two strands of half-DNA and now you have two copies of the same information coded as each others' inverse, you don't have double the information. (It also provides some resiliency- if one half of the DNA pair is damaged you can reconstruct it from the other half.)
I would make an objection to your summary of viruses and DNA, as they can actually hold a lot of it. There are things such as the Megavirus containing 1.2 million base pairs in its genome, or the Pandoraviruses which can have up to 2.5 million base pairs in a genome. This is much smaller than the human genome (3,000 million base pairs) but much larger than some bacteria (Mycoplasma genitalium) with about 500,000 base pairs. 29
The smallest animal genome exists in nematodes with about 20,000,000 base pairs.
The key thing to understand is that viruses are not alive in the sense of cells. They do not breathe, consume food, or replicate on their own. They're a lot closer to self-replicating nanobots that lie dormant until some unlucky space traveler turns over the wrong rock- and then they swing into action using a mechanical process to replicate themselves and turn the hapless explorer into more virus material and spread it around as much as possible.
If you want a virus with 3x as much information, just make a virus with 3x as long DNA.
However, it's not really clear that longer DNA means more complex behavior either, so it's not really clear what you're getting at the end of the day. The nematodes I mentioned above have genomes as small as 20 million base pairs, while the smallest flowering plant genome is 40 million base pairs (twice as big) though I doubt most people would consider flowering plants to be more complex than nematodes. Similarly- there can be wildly different genome lengths in the animal kingdom among life forms that seem more or less complex than one another. Birds have about one third the genome length that humans do, for example, but they do some pretty amazing stuff that people can't do. The marbled lungfish has a genome that's about 40 times longer than the human genome, and I doubt that most people think that sifting through the mud for mollusks is particularly complex behavior compared to the folks at NASA. 335