I enjoyed what you wrote but it didn’t answer my question. Could Hippolytus not be referring to Jesus as that Ark of Noah? This ark was compared to baptism. Why is it assumed that it was the Ark of the Covenant. It makes more sense to me that it was Noah’s Ark. As someone pointed out, God does not carry God. God does save as Noah’s Ark did.
Oh, my apologies for the misunderstanding

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It seems that the original quote was from a source that paraphrased the actual quote. Here is the full text from
newadvent.org:
“And, moreover, the ark made of imperishable wood was the Saviour Himself. For by this was signified the imperishable and incorruptible tabernacle of (the Lord) Himself, which gendered no corruption of sin. For the sinner, indeed, makes this confession: “My wounds stank, and were corrupt, because of my foolishness.” But the Lord was without sin, made of imperishable wood, as regards His humanity; that is, of the virgin (Mary) and the Holy Ghost inwardly, and outwardly of the word of God, like an ark overlaid with purest gold.” - From the Commentary by the Holy Bishop and Martyr Hippolytus, on “The Lord is My Shepherd.”
It is from a commentary on Psalm 22 and 23, and is part of surviving fragments.
Psalm 23 does seem to have references to baptism, and the apostles connected baptism to Noah and the ark (I Peter 3:20-22). But it is definitely talking about Jesus. It refers to the a rod (Rod of Aaron [Hebrews 9:4], which was kept in the Ark of the Covenant), anointing of oil, because Kings, the High Priest, and prophets were anointed with oil (1 Samuel 16:1, Leviticus 4:3-5, 4:16; 6:20; Psalm 132:10, Psalm 45:7, Psalm 89:20, 1 Kings 19:16; 1 Chronicles 16:22; Psalm 105:15, Ecclesiastes 9:8, Isaiah 57:9), and Jesus was anointed with oil (John 11:1-2, Matthew 26:6-13,Mark 14:3-9)
Anointing a king was equivalent to crowning him; in fact, in Israel a crown was not required (1 Samuel 16:13; 2 Samuel 2:4, etc.). Thus Saul (1 Sam 10:1) and David were anointed as kings by the prophet Samuel:
Code:
Then Samuel took the horn of oil, and anointed him in the midst of his brethren: and the Spirit of the Lord came upon David from that day forward. So Samuel rose up, and went to Ramah.—1 Samuel 16:13.
In the Catholic Church a person is anointed with oil at their baptism.
So, could Hippolytus be talking about the ark of Noah? The answer is no, because Hippolytus refers to Mary as being like the pure gold that overlaid the pure wood of the Ark of the Covenant. The outer portion of the Ark was not defiled while the inner portions were undefiled. He could not be possibly talking about Noah’s ark, because Noah’s ark was not overlaid with gold.
Source:
newadvent.org/fathers/0502.htm