I have the installed the same BI Publisher Desktop 11g (22.214.171.124.0) of 32 bit for Windows 7 64-bit. Just add the below code in your configuration setting file of your oracle BI publisher standalone(server side)-> install-> there you can find a file called oraparam.ini (its a configuration settings file).
#You can customise error message shown for failure, provide value for CERTIFIED_VERSION_FAILURE_MESSAGE
# Minimum display colours for OUI to run
MIN_DISPLAY_COLORS = 256
# Minimum CPU speed required for OUI
# CPU = 300
Red mark is the code which you need to add in the configuration file. black marked code is the code which already exiting in the file.
add this code before installing the desktop. then try to install. this time the software will install successfully.