At 20mA, that's about 120 Ohms. The current gain depends on the collector current, but figure on 50. With a base current of 20mA, that's a collector current of way more than the 2N3904 can handle, so 20mA will saturate it thoroughly. You can probably get by with a lower base current. Look at a 2N3904 datasheet for gain at different collector ...

2N3904 General Purpose Transistors NPN TO-92 Page 1 31/05/05 V1.0 High Speed Switching Features: • NPN Silicon Planar Switching Transistors. • Fast switching devices exhibiting short turn-off and low saturation voltage characteristics.