As far as sniper rifles go: You could have done worse. The Double Eagle L96 is based on/cloned from the APS Type 96 design, which is basically the second most used and supported bolt action configuration/specification next to the TM VSR.
So basically what I'm saying is your L96 is highly upgradable and there's plenty out there on making it perform a bit better (such as the 'TDC' mod, homemade barrel spacers, barrel polishing and piston dampening). If you're motivated enough then you can get good consistency out of your gun with just a handful of cheap parts, or you could double-down and start with the semi-expensive upgrades like a 90 degree trigger and piston.
Ultimately though the issue is that sniping in airsoft can require a significant amount of money to get right and skirmishing with it will be hard when you're up against AEGs that can shoot just as far as you. It's for that reason that BASRs are rarely recommended as a good 'starter gun'.
All airsoft sniper rifles are basically meh out of the box. What you need to decide now is if sniping is even for you (which is far easier if you have an AEG to fall back on). There's a slim chance you'll do ok even with your current stock L96, but there's a good chance you won't. Just don't be deterred from airsoft if you have a bad time - just put that money into an entry-level AEG if it's crap.