Assign capabilities to a new role for a custom post type

I want to allow a specific user role (and administrators) to edit their own custom post type.

I created my functions. Actually Administrator seems to have a full-access while the new role doesn’t have any access (can’t see the menu item nor access the wp-admin/edit.php?post_type=membres url)

// Register Custom Post Type
	function custom_membres() {

		$capabilities = array(
		 'publish_posts' => 'publish_membres',
		 'edit_posts' => 'edit_membres',
		 'edit_others_posts' => 'edit_others_membres',
		 'delete_posts' => 'delete_membres',
		 'delete_others_posts' => 'delete_others_membres',
		 'read_private_posts' => 'read_private_membres',
		 'edit_post' => 'edit_membres',
		 'delete_post' => 'delete_membres',
		 'read_post' => 'read_membres'
		);

		$labels = array(
			'name'                => 'Membres',
			'singular_name'       => 'Membre',
			'menu_name'           => 'Membres',
			'name_admin_bar'      => 'Membres',
			'parent_item_colon'   => 'Item parent:',
			'all_items'           => 'Tous les membres',
			'add_new_item'        => 'Ajouter',
			'add_new'             => 'Ajouter',
			'new_item'            => 'Nouveau',
			'edit_item'           => 'Modifier',
			'update_item'         => 'Mettre à jour',
			'view_item'           => 'Voir',
			'search_items'        => 'Recherche',
			'not_found'           => 'Rien trouvé',
			'not_found_in_trash'  => 'Rien trouvé',
		);
		$args = array(
			'label'               => 'Membre',
			'description'         => 'Tous les membres',
			'labels'              => $labels,
			'supports'            => array( 'title', 'editor', 'author'),
			'taxonomies'          => array(  ),
			'hierarchical'        => true,
			'public'              => true,
			'show_ui'             => true,
			'show_in_menu'        => true,
			'menu_position'       => 5,
			'menu_icon'           => 'dashicons-universal-access',
			'show_in_admin_bar'   => true,
			'show_in_nav_menus'   => true,
			'can_export'          => true,
			'has_archive'         => true,
			'exclude_from_search' => false,
			'publicly_queryable'  => true,
			'capability_type' => 'membres',
	        'capabilities' => $capabilities,

		);
		register_post_type( 'membres', $args );

	}
	add_action( 'init', 'custom_membres', 0 );

	// Ajout des r?les et permissions pour les membres
	add_action('admin_init','membres_add_gestionnairemembre_role',999);
	function membres_add_gestionnairemembre_role() {
	 add_role('gestionnairemembre',
	          'Administrateur des membres',
		    array(
		        'publish_membres' => true,
		        'edit_membres' => true,
		        'edit_others_membres' => true,
		        'delete_membres' => true,
		        'delete_others_membres' => true,
		        'read_private_membres' => true,
		        'edit_membres' => true,
		        'delete_membres' => true,
		        'read_membres' => true,
		    )
	    );
	}

What should I modify?