Does the 320i have an engine cover?
I have seen this engine cover issue with a Mercedes Diesel, the cover came a little loose and the diesel rattle was more pronounced, when it was put back on properly, the engine sounded much better.
'05 E90 325i 6sp Man SG 118,032km on the odo (retired) | '06 E90 325i Step SG 121,021km on the odo (retired)
'08 E90 325i LCI Step SG 130,024km on the odo (retired)
'13 D30 328i M-Sport Step | Estoril Blue | Black/Aluminimum | Pro Nav | Xenon HBA | Lane Change Assist 1,760km on the odo