Code P0135

P0135 is the O2 sensor heater circuit malfunction code. Basically it says that there is a problem with the heater inside the sensor not working properly.
That can be a bad sensor itself with a failed heater in it. Or it can be a problem with the wiring going to the O2 sensor.
I am surprised it does not show two codes with the sensor unplugged.

Testing is simple. You need a test light and the attached wiring diagram. https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester
Disconnect the sensor and use the test light to test for battery voltage on the red wire with yellow stripe (positive power) and the blue wire with red stripe (ground switched by the ECM). With the key on you should have battery power on those two.

You can also test the two wires that go to the sensor itself. For that you use a VOM set on resistance to touch the two heater contacts. A bad/open heater will show an open circuit while a good heater will show a resistance of 11 - 18 Ohms.
You can also check the sensor side it should show about 4.5 - 8.0 Ohms.

https://www.2carpros.com/articles/how-to-use-a-voltmeter

If you have power with the key on, the problem is probably the sensor itself.
If you do not have power then it is possible that the positive side (red/yellow) is broken between the sensor connector and the power relay for the injection system. Or the switched ground side (blue/red) wire is open or the ECM transistor is bad.

That can also be checked by measuring the continuity of the wires using the meter but I doubt you will need that.