This is the one Church of Christ which in the Creed is professed as one, holy, catholic and apostolic, which our Saviour, after His Resurrection, commissioned Peter to shepherd, and him and the other apostles to extend and direct with authority, which He erected for all ages as "the pillar and mainstay of the truth". This Church constituted and organized in the world as a society, subsists in the Catholic Church, which is governed by the successor of Peter and by the Bishops in communion with him, although many elements of sanctification and of truth are found outside of its visible structure. These elements, as gifts belonging to the Church of Christ, are forces impelling toward catholic unity...
Israel according to the flesh, which wandered as an exile in the desert, was already called the Church of God. So likewise the new Israel which while living in this present age goes in search of a future and abiding city is called the Church of Christ. For He has bought it for Himself with His blood, has filled it with His Spirit and provided it with those means which befit it as a visible and social union. God gathered together as one all those who in faith look upon Jesus as the author of salvation and the source of unity and peace, and established them as the Church that for each and all it may be the visible sacrament of this saving unity. While it transcends all limits of time and confines of race, the Church is destined to extend to all regions of the earth and so enters into the history of mankind. Moving forward through trial and tribulation, the Church is strengthened by the power of God's grace, which was promised to her by the Lord, so that in the weakness of the flesh she may not waver from perfect fidelity, but remain a bride worthy of her Lord, and moved by the Holy Spirit may never cease to renew herself, until through the Cross she arrives at the light which knows no setting. (Emphasis is mine)
Cf.
Dogmatische Konstitution über die Kirche LUMEN GENTUIM