can I look up the maximum value in 2 columns?

Can I look up the maximum value in two columns?

Cell I3 to I5 have basically this code

=MAX(D14:D108)

is the code I used but I had to split the table so now I need it to also show the max value in column K14:K108.

Cells J3 to J5 look up those values and return the date in column A

=INDEX($C$14:$C$1009,MATCH($I$3,$D$14:$D$1009,0))

currently looks up D but I need it to look up column K as well (in this formula)