I've managed to get a solution using 10 4s, as opposed to 11, might be fun to see the equation which uses the fewest number of 4s.
Here's mine:
44^(sqrt(4))+(4*4!)-(4*4)-4-(4/4)
Which gives
44^2+(4*24)-16-4-1
=
1936+96-16-4-1 =2011

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