You can apply for Z visa if you have the below two documents which obtained by your employer:
1. A visa notification issued by the authorized Chinese unit.
2. An originial and a photocopy of the Work Permit for Aliens issued by the Chinese Labor Ministry or the original of Foreign Expert's License issued by the Chinese Foreign Expert Bureau.
otherwise, you can't apply for Z visa, you can apply for L visa, you can demand 90 days stay duration on the visa application form. In principal, L visa holders are not allowed to work in China, however, police won't check it in most situations.

To get a China work visa, it is quite complicated and time-consuming. Please refer to the following link for more details http://us.china-embassy.org/eng/hzqz/zgqz/t84245.htm

Since you will be in China for only 3 months, you can try to apply for a visa with longer duration. You'd better get an F visa, instead of an L visa.