P0135 is for the heater circuit in the O2 sensor, Bank 1 Sensor 1 (up front). This will not cause you any drive-ability issues, but it will return eventually. Its almost always the sensor itself that is at fault but can also be the wiring or the pcm.
The pcm determines if the heater is working by measuring the current that flows through the heater circuit while it is commanded on. You can check its resistance to get an idea if its totally screwed or not, if you disconnect the connector with the O2 sensor cold and measure with an ohmmeter between the 2 black wires(may be white, but there are 2 like colored wires in the 4 wire connector) You should see 10-15 ohms resistance. If it is out of spec with this, you will need to replace it. I don't recommend after market o2 sensors, especially for Honda heater codes, they are very picky. If you cant afford an OEM sensor you can use an NGK/NTK or Denso sensor as they are the manufacturer of the OE part. They are not too hard to change, but depending on accessibility you may need an O2 socket. The hex nut is 22mm(7/8").