Looking up new bar codes and matching to product.

See attached sheets:

New product codes (sheet 2- Horizontal rows B1 through E10 need to be applied to products on sheet 1 according to size (vertical column F)...the common name (product color) is in column 1 on code sheet 2...matching the same name repeated for each of the four sizes in column 4 on product sheet.

The problem is coming up with a formula that places all the correct codes on the product sheet in column K...and being able to copy it down for several hundred different products.

I've tried multiple ways with both VLOOKUP and INDEX/MATCH combos without success.

Any help much appreciated.
Thanks

code matching to products.xlsx