You should be able to contact Winchester and see if you may find the year of production by serial number thru there archives.If not I do have the manufacture dates of the first 250,000 made.You will need to have your serial number available to research the date of manufacture.
You did not give the correct serial number. Winchester stopped making the Winchester 94 in 1982 and the last serial number was 5103248. Recheck your serial and search by Winchester date of manufacture.
Your winchester should have a model number located on the firearm.This will greatly help in producing a date of manufacture along with the serial number 389,455.Please include this info in your question.
If you would provide the serial number to your winchester rifle,I could give you the date of manufacture. 218895.With the serial number that you have provided,your Winchester model 1894 rifle was made in the year 1901.