Failed emissions test

My '92 Metro failed the emission test with an Hc of 560. They said 220 is the limit, and that a lot of unburned gas was going out the tailpipe. The car has 296K on the motor, but is in good shape (175# on all 3 cyls). No check engine lights - car seems to run good. Daughter says she only gets about 37 MPG. I figured the drop in MPG is due to the teenage lead foot. Over a year ago, I was getting over 50 MPG. This is the first time the car has been emission tested. I'm thinking about changing the -02 sensor, but question why if indeed it is bad, no CEL light? Plugs, cap, rotor, wires are new. New injector has less that 30K on it.
Any thoughts would be appreciated.
Thanks,

Everything points to a worn out engine, you sure about that compression test?

O2 sensor could be off, not dead. The PCM only knows if the O2 sensor sends completely ridiculous information, if it's reporting .6 volts when the truth is .4 volts, the computer would never know. O2 for a 92 should be quite cheap, can't hurt to change it. Start spraying it with Kroil or PBlaster now to help get it out.

Try advancing your timing, gives the air/fuel more time to burn before the exhaust valve opens. DO NOT PUT "PREMIUM" GAS IN IT This is a common mistake people make trying to get through an emissions test, premium gas burns slower and will exacerbate your problem.

Remember that oil is an unburned hydrocarbon too.