DNA System: The complete cellular system that processes the genetic instructions and data stored in DNA. That would be the cell, then? You can't process the instructions without enzymes, you can't make enzymes without making the amino-acid building blocks, you need the cell membrane to keep everything in, etc.. There are very few parts of a bacterial cell you can lose without losing the functions of transcription and replication.
All this system does is try to replicate itself. It exists to make an exact copy of itself. The genetic instructions and code's role is to produce an exact, working duplicate.
"All this system does is try to replicate itself. It exists to make an exact copy of itself. The genetic instructions and code's role is to produce an exact, working duplicate." 
More precisely, the cellular system / DNA system will produce WHATEVER the genetic instructions/code/data tell it to produce.
This is why humans can CHANGE the genetic code in DNA to custom tailor different living outputs/results.
If we insert an EXIT SUB genetic marker into the beginning of a gene, then the cellular system will obey our command and turn that gene off by ignoring the execution of subsequent genetic instructions in that part of the DNA.
And the more that we learn and understand about this genetic code, the better medicines (among other things) we will be able to design and produce.