I think it also has some processing capability as well.

There are also different levels of data encoding. The four bases form letters that spell out typographical commands, long strings of bases denote proteins and their structure, plus special characters with grammatical and punctuation functions. But there is also a secondary structure formed by kinks and twists in the chain, and a tertiary structure at larger scales, and there are probably hgher levels too.

We know how proteins are encoded in DNA, just like the chemical formula for concrete might be written on a blueprint. But how does the DNA encode the macro architectural details of blood vessels, muscles, bones, etc. These are the arches, columns, floors and walls
of the body. Not only the structural details, but the assembly instructions must somehow be encoded too. You don't hang the roof before you pour the foundations! The embryological development of an organism has to be specified in DNA, and somehow communicated to the reproductive organs. There is a lot going on we don't understand.

No, natural selection is not "wrong", but it must only be the tip of the iceberg.