Compile time polymorphism with enums

So, the questions is related to enum inheritance, and i seen a lot of topics here, in which described approaches how to write enum that support inheritance, but it is not the my case, I think.

I found some stuff that I would want to make. So the idea is that I have the class, let it be OpenGL texture class (actually it is) and there is enum that represent all possible values of one property in texture.

class Texture
{
    public:
        enum Filter
        {
            LINEAR   = 1,
            BILINEAR = 2,
            ANISOTROPIC = 3
        };

    public:
        Texture(Filter _filter)
            : filter(_filter) 
        { }

    private:
        Filter filter;
};

And class that inherits it. Enum in derived class must be redefined, but that I can use further in base class's constructor:

class Texture2d : public Texture
{
    public:
        enum Filter
        {
            LINEAR   = 1,
            BILINEAR = 2
        };

    public:
        Texture2d(Filter _filter)
            : Texture(_filter)
        { }
};

but, of course, this doesn't work, because newly created Filter is Texture2d::Filter, but not the Texture::Filter.

I tried to use an enum class like this:

class Texture
{
    public:
        enum class Filter;

    public:
        Texture(Filter _filter)
            : filter(_filter)
        { }

    private:
        Filter filter;
};

class Texture2d : public Texture
{
    public:
        enum Filter
        {
            LINEAR = 1,
            BILINEAR = 2
        };

    public:
        Texture2d(Filter _filter)
            : Texture(_filter)
        { }
};

But this is really stupid idea. I think, if I just would want to expand enum I would write some class wrapper, but I need to shrink enum too. So the question is, how to make this thing work on compile time? It is main problem - make this work in compile time. And another one question: actually trying to do such stuff is ok or I must check out architecture of my application?

(All answers will be appreciated)