That is all well and good, but we represent things all of the time when we draw it, write about it, speak about it or think about it. We can even imagine improving it. The fact is everything that man has built started out as a concept. Even a rock used as a weapon had to be conceived even if it was initially picked up to be used as food.
As for DNA coding, anything can be used to represent something else because representation is a concept(written while moving salt shaker to the left and stating this is New York). Eyeblinks were used to send a message by a POW. You want to code the human genome by drumbeats, it can be done, but you better have a lot of time to waste.
You want to use DNA to code a program? That is easy. With 4 bases ,
1100110100000111
In DNA code mapped as above this would be
TATCAACT
As you can see each byte takes up 4 bases, so that a DNA the size of the Human genome could code a program of about 750 megabytes. In this day and age it may seem like a trivial amount of data since it will easily fit on a DVD. However, going through all of the progrms that could be written in that amount of memory would take a very long time. Here is a previous calculation giving an indication of the information that can be coded by the DNA.
The number of different items represented by that 6 billion bit sequence as I stated before is 26000000000. In base 10 that would be 101806179974. Now there are 60 seconds/minute * 60 minutes/hour * 24 hours/day * 366 days/year * 15,000,000,000 years = 4.74336E+17 (or 1017.67608609) seconds since the purported start of the universe. We will assume this full time is available to generate the sequences represented by the 6 billion bit sequence. The huge number represented by 101806179974 breaks all my calculators so I must use logs. If we divide the number of items (101806179974) by the time available (1017.67608609) we end up with 101806179956 combinations/second. Clearly that is a huge amount of "information".