Hi liron,
1. 0x3D is nothing special to the ADXL362. I would suggest you to check the program to see whether there is some conflict on the SPI interface. The power supply can be monitored too, to see whether there is jump on it when you see 0x3D in the position where 0x3D should not shown.
2. The self test procedure that you described is a little different from the recommended one. Please check the USING SELF TEST section on page 41 of datasheet. You can set ODR to 100Hz.
Hope these can help.
BR
Neil