Actually this sounds like it is probably within the tolerance of your accelerometer.
All such devices have some sort of offset error, however small, and must be calibrated for maximum accuracy.
For example, the Memsic MXA2050A specifies a maximum offset of plus or minus 0.6 g... for a 10g device that means a maximum offset of 6 percent.
78 'counts' out of 1024 implies an offset tolerance of 7.6 percent, so I wouldn't get too bent out of shape about this unless I paid for greater tolerance, and making very sure the device was really, truly level when measuring the offset.