Junior with 3.76 sGPA and 3.78 overall! Improve my chances?

Hi guys,
I just wanted to hear some feedback of getting into med school this spring.
I go to a top 15 Undergrad school in the midwest and got out with a 3.76 science gpa and 3.78 overall this semester. I am planning to take the MCAT in the spring and was wondering if I had a shot at any of the top 20 medical schools. I know that numbers are not the only thing they are looking for but I want to know if I can step my foot in the door.
I was hoping to try really hard and raise my science GPA to a 3.8 next semester and was wondering what MCAT score I should aim for to make me competitive for a top 20 medical school?
Thanks guys

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Junior with 3.76 sGPA and 3.78 overall! Improve my chances?