Best way to represent game card class in C#

Question

I use class Card which contains 2 enumerated properties (suite - hearts diamonds spades and clubs) and card value from 2 to A. And overrides ToString() method to returns som

Answer 1

Couldn't you assign Jack, Queen, King, and Ace to be 11, 12, 13, and 14, respectively? It'd end up looking something like:

public class Card
{
    public int Value { get; private set; }
    public enum SuitType
    {
        Clubs, Spades, Hearts, Diamonds
    }
    public SuitType Suit { get; private set; }
    public Card(int value, SuitType suit)
    {
        Suit = suit;
        Value = value;
    }
    public Card(string input)
    {
        if (input == null || input.Length < 2 || input.Length > 2)
            throw new ArgumentException();
        switch (input[0])
        {
            case 'C': case 'c':
                Suit = SuitType.Clubs;
                break;
            case 'S': case 's':
                Suit = SuitType.Spades;
                break;
            case 'H': case 'h':
                Suit = SuitType.Hearts;
                break;
            case 'D': case 'd':
                Suit = SuitType.Diamonds;
                break;
            default:
                throw new ArgumentException();
        }
        int uncheckedValue = (int)input[1];
        if (uncheckedValue > 14 || uncheckedValue < 1)
            throw new ArgumentException();
        Value = uncheckedValue;
    }
    public string encode()
    {
        string encodedCard = "";
        switch (Suit)
        {
            case SuitType.Clubs:
                encodedCard += 'c';
                break;
            case SuitType.Spades:
                encodedCard += 's';
                break;
            case SuitType.Hearts:
                encodedCard += 'h';
                break;
            case SuitType.Diamonds:
                encodedCard += 'd';
                break;
        }
        encodedCard += (char) Value;
        return encodedCard;
    }
    public override string ToString()
    {
        string output = "";
        if (Value > 10)
        {
            switch (Value)
            {
                case 11:
                    output += "Jack";
                    break;
                case 12:
                    output += "Queen";
                    break;
                case 13:
                    output += "King";
                    break;
                case 14:
                    output += "Ace";
                    break;
            }
        }
        else
        {
            output += Value;
        }
        output += " of " + System.Enum.GetName(typeof(SuitType), Suit);
        return output;
    }
}

Edit: I added some string functionality. I took structure of Card(string input) from Jon Hanna's answer.