Hello Philipp,
It seems to be more a hardware than software problem but anyway, Pull-up resistors are enabled in usb_dci_khci_init funcion at khci_dev.c file (located at usbd_sd_bm_lib_MK64F12 > usb_core > device > sources > controller_driver > khci
/* Weak pull downs */
usb_hal_khci_set_weak_pulldown(usb_dev_ptr->usbRegBase);
/* reset USB CTRL register */
usb_hal_khci_reset_control_register(usb_dev_ptr->usbRegBase);
/* Enable internal pull-up resistor */
usb_hal_khci_set_internal_pullup(usb_dev_ptr->usbRegBase);
usb_hal_khci_set_trc0(usb_dev_ptr->usbRegBase); /* Software must set this bit to 1 */
Other importat thing to be considered is that USB's clock should be set to 48 MHz and CPU's clock must be greater than 20 MHz in order to work properly. Also, here are other "common" errors that avoid USB Device to be recognized by PC:
KDS/KSDK K20 USB Driver Mutex Problem
PE-generated USB code does not seem to work
For hardware's point of view, It is important to add a Capacitor on VOUT33 terminal.

Also, make sure that USB hardware is similir to the one used in FRDM-K64F:

I hope this helps!
Regards,
Isaac