If you put your data into an organism's "junk DNA", then the data will last forever... (barring mutations)
Very little "Junk DNA" is junk. miRNAs, gene regulatory regions, histone folding and regulation systems, chromatin folding hotspots. Anyway, if there is true Junk DNA, it will be under less selective pressure and very quickly become riddled with mutations and errors. Moreso than protein encoding regions. The best way to do it would to be to place an index somewhere in the genome containing references to locations within the existing coded/exome areas -- which already contain a pre-existing massive dictionary of 4-5-n base sequences. Mapping the data would be a bitch, but if you're that desperate to encode data long term, it might be worth it. Providing your mouse/rabbit/fly/c.elegans colony doesn't die in flood/heat/poisoning/infection etc.
May Euell Gibbons eat your only copy of the manual!