Its a big step up from the 20g you have now!
I had a 150g when I lived at home and sold it when I went flatting because I knew I wouldn't be settled for a few years (and I needed to upgrade for my 20"+ black aro, which I sold at the same time
). I've only just bought another big tank (160g) now that my gf has finished uni and we're not going to be moving for a while. Seems how your only 14 and probably have at least another 2-4 years at home you could get it as it sounds like a good deal, but just think about what you stock it with. Otherwise go for something in between line a 150/180g just to prove to them you're serious and will look after a big tank.
I had a 150g when I lived at home and sold it when I went flatting because I knew I wouldn't be settled for a few years (and I needed to upgrade for my 20"+ black aro, which I sold at the same time
and hopefully with my kind and well thought out words may come to your parents thoughts that they grant you the tank approval in accepting it into your hands with responsibity.