Building a CL command in a RPG Program (Help!)

I am trying to build a CL call command within a RPG program with four
parameters. I cannot get the command to work. I am modifying a program and
for some reason unable to debug it to verify the command is right. What is
the proper syntax for putting quotes around parameters? 

This is the command I want to call: 
SBMJOB CMD(CALL PGM(PGMNAME) PARM('PARM1' 'PARM2' 'PARM3' 'PARM4'))
JOB(JOBNAME)

This is the code I have to build it:
EVAL            CMD = 'SBMJOB CMD(CALL PGM(PGMNAME) ' + 
                'PARM("' + Parm1 + '" ' +                 
                '"' + Parm2 + '" ' +                      
                '"' + Parm3 + '" ' +                      
                '"' + Parm4 + '"))' +                      
                ' JOB(JOBNAME)'                             

The command is being passed to a CL where is then uses QCMDEXC to execute
the command. My program gets a data decimal error because on some of the
parameters, it picks up the double quotes as part of the parameter (ex. A
date field would look like "0501200).

Thanks for any help!

Mike
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