WebApi2 Google OAuth2 middleware error response

For user authentication with external providers such as Google, it is using specific Owin middlewares. As for example Microsoft.Owin.Security.Google. WebAPI2 template uses this to support implicit flow authentication (response_type=token). But what about Code flow?

Is it possible to implement Code flow (response_type=code)?

After debugging those OAuth providers I noticed that passing return_type=code to Google, it successfully authenticates and returns json with access and refresh tokens, then user gets signed in by api/Account/ExternalLogin endpoint but at the end of the flow I get redirected to http://localhost:50321/?error=unsupported_response_type#.

I could not really find the flow where and why it is setting this specific error in the assembly.

Startup.Auth.cs looks like this:

public void ConfigureAuth(IAppBuilder app)
    {
        app.UseExternalSignInCookie(DefaultAuthenticationTypes.ExternalCookie);

        PublicClientId = "self";
        var tokenTimeSpanInHours = ConfigurationManager.AppSettings["AccessTokenLifeTimeInHours"];

        OAuthServerOptions = new OAuthAuthorizationServerOptions
        {
            Provider = new ApplicationOAuthProvider(PublicClientId),
            TokenEndpointPath = new PathString("/api/token"),
            AuthorizeEndpointPath = new PathString("/api/Account/ExternalLogin"),
            AccessTokenExpireTimeSpan = TimeSpan.FromHours(Convert.ToInt16(tokenTimeSpanInHours)),
            AllowInsecureHttp = true
        };

        app.UseOAuthBearerTokens(OAuthServerOptions);
        var googleOAuthOptions = new GoogleOAuth2AuthenticationOptions
        {
            AccessType = "offline",
            Provider = new CustomGoogleAuthProvider(),
            ClientId = ConfigurationManager.AppSettings["GoogleAccountClientId"].ToString(),
            ClientSecret = ConfigurationManager.AppSettings["GoogleAccountClientSecret"].ToString()           
        };
        googleOAuthOptions.Scope.Add("profile");
        googleOAuthOptions.Scope.Add("email");
        googleOAuthOptions.Scope.Add("https://www.googleapis.com/auth/gmail.send");
        app.UseGoogleAuthentication(googleOAuthOptions);
    }

Where is the problem then? Do I need some explicit configuration to tell that I want code flow? Is it supported?