What results are you expecting in the sample file? Does this one work?
Formula: copy to clipboard 
=IFERROR(LOOKUP(1E+100,FREQUENCY(IF(ISNUMBER(MATCH(C4:LT4,{"I","M","R"},0)),IF(C4:LT4<>"",COLUMN(C4:LT4))),IF(C4:LT4<>"R",IF(C4:LT4<>"M",IF(C4:LT4<>"I",IF(C4:LT4<>"",COLUMN(C4:LT4))))))),"")