C#でDataGridView.Columns[0]に自作プロパティを作成する方法

class1.cs

public class CusDataGridViewColumn: DataGridView
{
    public new List<CustumColumn> Columns { get; }

    public CustumColumn this[int index]  // インデクサ
    {
        get
        {
            return Columns[index];
        }
        set
        {
            Columns[index] = value;
        }
    }
}

public class CustumColumn : DataGridViewColumn
{
    public string test { get; set; }
}

Form1.cs

    private void Form1_Load(object sender, EventArgs e)
    {
        string a = cusDataGridViewColumn1.Columns[0].test;
        a = cusDataGridViewColumn1.Columns[1].test;
    }