Get the numbers from (0-30) by using the number $2$ four times

How can I get the numbers from (0-30) by using the number $2$ four times.Use any common mathematical function and the (+,-,*,/,^) I tried to solve this puzzle, but I couldn't solve it completely. Some of my results were: $$2/2-2/2=0$$ $$(2*2)/(2*2)=1$$ $$2/2+2/2=2$$ $$2^2-2/2=3$$ $$\frac{2*2}{2}+2=4$$ $$2^2+2/2=5$$ $$2^2*2-2=6$$ $$\frac{2^{2*2}}{2}=8$$ $$(2+2/2)^2=9$$ $$2*2*2+2=10$$ $$2*2*2*2=16$$ $$22+2/2=23$$ $$(2+2)!+2/2=25$$ $$(2+2)!+2+2=28$$

Solution 1:

$14=2^{2^2}-2$
and
$18=2^{2^2}+2$
$13=\frac{22}2+2$
$24=\frac{(2^2)!}{\frac22}$
$20=\sqrt{{22}^2}-2=(2^2)!-2^2$
$22=\sqrt{\left[(2^2)!-2\right]^2}$

Solution 2:

Though I suspect this may be pushing common functions..

$2^2 + 2 + \Gamma(2) = 7$

$22/{\sqrt{2}^2} = 11$

$\int_{2/2}^{22}dx =21$

$\int_{2-2}^{22}dx =22$

$(2+2)! + \sqrt{2+2} = 26$