If you only want to know with what hands to call the 4-bet shove, then we're doing this the wrong way.

Villain's range is { TT+,AK,AQs }.
Hero faces a bet of 88 into a pot of (113.5 - rake)
bet/(bet+pot) = 88/(201.5 - rake) ~= 44%

Hero calls with any hand which has at least 44% equity against Villan's range.
{ JJ+, AKs }

Knowing the rake on a pot this size would help narrow down that 44%.

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If you want to know what range to 3-bet, then we also need to know:
What's Villain's range to open UTG?