Lenders won't lend more than what the house Appraises for - not what the assessment is. The assessment is not necessarily the current market value - which an appraisal is.
Banks will only loan money up to the appraised value. In you case, they'd lend 22k and you'd have to pay the difference in cash.
Finding someone to do a loan for 22k is going to be extremely difficult, too.
Let me know if you need anything.