Making a tetris clone, what to do about the grid?

Question

I want to make a tetris clone as a personal project. I am using a windows form app. My picturebox is 250 x 500 pixels, making each square 25px x 25px. I have already made my tetris pieces using photoshop, and they are in .png format.

Now, the main reason I am posting this is to get an idea of how the game grid works. I know that its going to be a 2D array. What I have so far...

namespace tetris
{
public class GameGrid : PictureBox
{
//multidimensional array because we have a grid
private int[,] grid{get; set;}
private int x;
private int y;

public GameGrid()
{
grid = new int[10,20];//our grid is 10 x 20
}
}

Basically, do I inherit the PictureBox properties or not? since I want to model the grid as a 2D array.