My solution:
=INDEX($A$2:$A$5,MATCH(MIN(IF(($B$2:$B$5)="J",($C$ 2:$C$5))),($C$2:$C$5)
*(($B$2:$B$5)="J"),0))
works fine becouse target are "fltered" for "J".

this is good point! thank you for help Scossa it works great now. Thank you
also Bernard for explanation.
I've got another problem in my real excel data. I'm using outline in every
row and this array formula is being used inside it, so pressing ctrl,shift
and enter gives me an error.

Going back to my example add a row between rows C1 nad C5 and try to put
this array formula in C3. You will get an error after pressing
ctrl+shift+enter. How to exclude the whole row which contains this array
formula from its range?