There are great prebuilt lights for your 2x2. Ready to hamg and grow.
Do it yourself may not save money IMO.
2x2=4sq ft.
35watts per sq ft is a general rule.
So you need about 140watts of lighting.
DIY
For a 2x2. A pair of these side by side would fit physically. Or just build a single unit 22x22 with x number of strips.