If I interpret your question correctly -- and you were not in a parking
area which was painted either red or yellow -- in my opinion, you do
have a legal cause of action against whatever entity and/or person
authorized your vehicle to be towed.
It may well be that the City Water Department or Police Department for
some other city government entity had your vehicle code. If this
is the case, I recommend that you go directly to that city Department
and formally ask for a reimbursement of your towing costs.
On the other hand, if a non-government type -- like a building manager
or landlord -- authorized the total, given the presumably small sum of
money involved, I recommend that you file a claim in Small Claims
Court. You represent yourself in small claims -- so the
proceedings are less formal than 'regular' court.
The lawyers are allowed that you can bring a friend. You can also present evidence and (if you have any) witnesses.
That said, unless you have witnesses (or their signed statements) or
photographs -- it would seem to come down to your word against the word
of the defendant(s).
The fees to file a claim in Small Claims Court are relatively small,
and if you prevail, you should be able to get a judgment from the court
which directs the defendant to pay both your towing and court fees.
Let me know if you need more input. If not, thanks for the
opportunity to assist you... I would really appreciate your honoring my
efforts by 'pushing the button' and Accepting this answer. Adding
a bonus -- should you wish to do so -- is always warmly welcomed.