Hello V_merino

VM>>
'TX PIC:
Include "modedefs.bas"
pause 1000
SEROUT 0, T2400,[%11100010]
END

'RX PIC:
SERIN 3,T2400,10000,error,RX 'wait for signal for 10 seconds
LCDout #RX
goto finish

error:
LCDout $fe, 1 'clear screen
LCDout $fe, 2 'return home
Lcdout "Error"

finish:
end
<<

Make sure your RX pin is a data pin in the TRIS registser, and make sure your TX pin is a output pin in the TRIS register.
I don't see any of this in your program.

Then I would try for the SIMPLER SERIN and SEROUT (until you can verify your data is actually being sent in good form..
Use
Serin Pin, T2400, RecDataword

Serout Pin, T2400, DataWord


With this verified, then put your "Flags and timers on". You could have "noise" going on from improper grounding, and that will give you trash.