You seem well qualified, but as @paraguas and @Dndaniell16 said, you still have a low chance of getting in. Remember, Stanford is the hardest college in the country to get into and they are looking to fill only about 1700 spots (about 1550 of which will be US students).
Think about that for a second. There are about 37,000 public and private high schools in the US (see http://www2.ed.gov/about/offices/list/ovae/pi/hs/hsfacts.html) So, statistically speaking, Stanford is not trying to draw the best student out of each US high school; they are seeking to draw the best student out every group of 24 US high schools. (My own high school, which had over 4,000 students, saw a student admitted to Stanford about once every 7 years.)
Similarly, there are probably 13,000 or more students with 2240 SATs or better (plus many more who scored as well or better on the ACT). A substantial percentage of those students are going to have perfect or near perfect grades too.
I think it is worth applying, but as the saying goes, if there is only a 5% chance of rain you shouldn’t walk around in your rain coat all day.