In the human genome there are around 1,800,000,000,000 daltons, weighing about 0.000000000000000002988954 grams which stores about 1.5 GB of data; though I do not currently have data on the most efficient weight:data ratio of artificial data storage mechanisms I would be more than willing to concede that DNA is likely far FAR more efficient a storage mechanism than anything we have yet devised, gram for gram,
but that is not what you first said and your amendment substantively alters what you proposed.
The mass of DNA, proteins and other organic molecules is usually expressed in Daltons. A Dalton, also known as an atomic mass unit, is roughly the mass of a single proton or neutron. In relation to other units of mass, a Dalton is one-thousandth of a zeptogram, which is one-thousandth of an attogram, which is one-thousandth of a femtogram, which is one-thousandth of a picogram, which is one-thousandth of a nanogram, which is a billionth of a gram.
Mass DNA molecules
Every base pair in a DNA molecule contributes about 600 Daltons (1 Dalton = 1 atomic mass unit) to the molecular weight of a DNA molecule
Molecular Weight of DNA
human genome (contained in egg and sperm cells) consists of three billion DNA base pairs,
http://en.wikipedia.org/wiki/Human_genome
6×10^9 base pairs/diploid genome x 1 byte/4 base pairs = 1.5×10^9 bytes or 1.5 Gigabytes
How Much Information is Stored in the Human Genome? | Bitesize Bio
It is true our current technological innovations have not yet reached the extremely high rates of efficiency present in the sub molecular encoding standard that is DNA as you have recognized. But then again, what of it? If you were to create an appropriate systematic way of decoding the molecular structure of a rock, it could present similar gram for gram data (because it would contain a similar number of daltons and thus sub molecular components - in fact given the need to model the distribution of those components, the rock might actually incorporate a higher degree of geospatial data), likewise, we may one day develop the ability to create and utilise atomic level data encapsulation and encoding. We are not there yet and it may well prove impractical for whatever reasons (energy use for example) however this would in no way whatsoever support the assertion of a designer... it is simply not relevant.