Can I marry my second cousin (from maternal side)

The Hindu Marriage Act, 1955 prohibits marriage between persons of Sapinda relationship. If valid custom is there then only that marriage is allowed. The customs that are valid are mentioned in Section 3 of the Act. Sapinda Marriages are liable for punishment under Section 18(b) of the Act. The punishment may be simple imprisonment for one month, or one thousand rupees fine or with both.
As per Section 3 (f)(i) of the Hindu Marriage Act, 1955 'Sapinda relationship' will extend up to the third generation (inclusive) in the line of ascent through mother, and extend up to the fifth-generation (inclusive) in the line of ascent through father
You, your mother, your grandmother and her mother. Starting from you it is 4 generations to have a common ancestor from your mother side. Your relationship will not come under Sapinda marriage. So legally you will not have a problem. You have to talk to your parents and the parents of the girl and then you can go ahead.

As mentioned above your relationship doesn't belong to sapinda relationship. So, you are legally free to make an alliance. According to Hindu marriage act 1955 those relationship which comes under sapinda relationship is not allowed. The Hindu Marriage Act, 1955 have modified the concept of Mitakshara and prohibits the marriage between persons of Sapinda relationship. Except such marriage which are permitted by valid custom or usage. Sapinda Relationship extends as far as 3rd generation in the line of ascent through the mother in case of both the parties. And it extends as far as 5th generation in the line of ascent through the father in case of both the parties. Since you are free from this restriction so you can talk with girls family. If they get agree then you should go ahead.

If your family and community follows the patriarchal system- i.e the family linage follows the father's side, then there is no problem for the marriage. However if your traditional family lineage is of mothers' side, then it may not be permitted by family tradition. So you take the opinion of your family elders.

If both families consent to that then go ahead, Best Wishes.

Examining your case it appears that you don't come under the purview of the sapinda relationship and as such you might take the next step for the finalisation of your marriage. There are a few points to be discussed both in your family and your second cousin with whom you have to settle your marriage relationship.The points are as follows-
1) Discuss the issues with your family as well as with the family of your would be spouse. There should not be any complexities in going ahead for such relationships.
2) Both of you are comfortable if the marriage is finalised.
3) If either of you are financially stable to support the responsibilities of the family.
4) Both of you can appreciate the feelings of each other and you may rely your partner in all respects.
5) If both of you undergo for the medical tests to know any abnormality that might hinder on the path of parenthood, both of you will remain relaxed. In case of any abnormality, you might need the consultation of the specialist.