16 bit DAC AT-60DB

I built a standard test board with a TDA1541A and NE5534 I/V, driven by an ESP8266-based I2S generator. Now I can send any test signal to the test board. I generated a 6-bit dithered ;) pure sine (-60 dB) and measured the output spectrum. What I observed is that the distortion depends on the upper bit values. Ex.: 0x7FFF FFFF FFxx xxxx is higher than 0x0000 0000 7Fxx xxxx etc. The best distortion I measured is below 0.1%, the worst is 0.28%, depending on the digital shift. The digital shift will cause analog DC shift after conversion. Transition between 0x7FFF FFFF FFFF FFFF to 0x8000 0000 0000 0000 is the analog zero, with 0.28% THD. But I found a method to reduce it :).