Your explanation of which two bits are not used seems implausible. Are you sure it is the most
significant 2 bits of the low byte which are unused ?
You may need to be shifting the first byte you read by 8 bits, not 6 bits, if that is the case.
If you only shift the first byte you read by six bits, then the second byte you read will overwrite
the least significant two bits of the first byte, which is probably not what you intended.
I'd suggest printing the actual hex value of the two bytes which you read to the serial monitor
and examining them closely, to check.