One of our basic tenets of faith in God, in the words of Maimonides: "He is not a body and not a power in a body."
God is both omnipresent and omnipotent. Maimonides explains that if He were corporal ("a body") He could not be omnipresent (in heavens above and earth below simultaneously and uniformly), and if He were a power vested in corporeality ("a power in a body") He could not be omnipotent (for His body would limit His power).
A body is a definition. God cannot be defined and so He possesses no body. All created beings can be defined; they all possess bodies, whether physical ones or spiritual ones.
The Bible speaks of God as being absolutely "unlike" anything in creation. Would He have a body, in that respect at least, He would be like everything else.
The gematria of "He is not a body" (אינו גוף) is 156 (6 times 26, God's essential Name Havayah), the identical gematria as that of the second half of the phrase, "and not a power in a body" (ולא כח בגוף)! Thus, the entire phrase = 312 = 12 times Havayah. The 4 letters of the Tetragrammaton, Havayah, permute in 12 different ways (corresponding to the soul-roots of the 12 tribes of Israel and the 12 months of the year, etc.).
All 12 permutations of God's essential Name Havayah proclaim "He is not a body and not a power in a body"!