Cool idea, but that would require a lot of money and is not technologically feasible currently, given that synthesized DNA can only be synthesized up to a couple thousand base pairs as limited by the current technology. Additionally, getting such a short DNA molecule to self replicate may prove difficult.
Another idea is to do polymerase chain reaction (PCR) using isotope labeled dNTPs (the nucleotides A, T, G, and C). Do one round of PCR, save that product, do a second round, save that product, etc until you have enough rounds of PCR (analogous to generations of E. coli) to do your very own Meselson-Stahl inspired experiment!
I don't really know much details about biology stuff, so just curious and nievely thought how about:
Synthesize something like isotopically labelled DNA plasmid (so with smaller number of DNA base pair) would it works? XDD
No need to synthesize the plasmid, you can just grow that plasmid in bacteria that have the isotope present in the media. But even then, the results would just say something about plasmid DNA replication :)