If I only cover the headbasket with aluminium foil, the disturbance is completely gone.
(Today I ordered a 10 dB attenuator to be placed between the timecode transmtter and the antenna. I hope this will solve the probem.)
U87 are virtually RF proof-they were specifically designed for RF-rich broadcast environments.
I would therefore try to first isolate a possible defect in the shield/ground coverage of the mic before moving outward.
Your eliminating the noise via basket shielding gives me pause: touch basket and XLR pin #1 of the mic with an ohm meter: zero ohms?