Registering a company in the UK while on Tier 2 General Vis

I have a question and would really appreciate your help.

I am Tier 2 General visa holder and work full time for my sponsor company. As a Tier 2 General visa holder can I register a new company in the UK and be a director of that company?

I will continue work at company that sponsors my Tier 2 Visa but would like to find out if there are any restrictions for registering new company in the UK in my name, being the director of it and having income from it.

Thank you a lot in advance!

No you cannot. You cannot be self employed on a Tier 2 General visa at all.

Technically there is no restriction on registering a company or owning shares in a company even if own them all.
The restriction is on "working". So you can register a company but you won't be able to work for it.