Read non-static property value of a subclass via Reflection

I am implementing a variation of the Command design pattern. I have an abstract CodedCommand class with some subclasses, each of one with an overriden "Code" property of type char. Each subclass has then the responsibility to "encapsulate" its own Code letter to which it is associated.

The use case is: when some serial parser receive a char/byte, I want to create an instance of the appropriate subclass, to further process the command payload.

My problem is: I don't know how to get the specific value from each subclass.

My current implementation is below. The problem, highlighted with a comment, is that type.GetProperty("Code") is returning null!

internal abstract class CodedCommand
{
    internal abstract char Code { get; }
}

internal class EventA : CodedCommand
{
    internal override char Code => 'A';
}

internal class EventB : CodedCommand
{
    internal override char Code => 'B';
}

public class CommandCreator
{
    Dictionary<char, Type> _typeMap 
        = new Dictionary<char, Type>();

    public CommandCreator()
    {
        var types = GetType().Assembly.GetTypes()
                                     .Where(type => type.IsSubclassOf(typeof(CodedCommand)))
                                     .Where(type => !type.IsAbstract);

        foreach (var type in types)
        {
            var field = type.GetProperty("Code");  // returns null!!!
            var value = field.GetValue(null);
            var code = (char)value;

            _typeMap[code] = type;
        }
    }


    CodedCommand BuildCommand(char code)
    {
        _typeMap.TryGetValue(code, out Type type);

        if (type != null)
        {
            return (CodedCommand)(Activator.CreateInstance(type));
        }

        return null;
    }
}

So my question is how can I fix this design?