Update, 2/12 3:47 PM PST: SiriusXMU have informed us that the new song will now be aired on Monday, around noon.
Sam G, and others, have informed us that SiriusXMU (channel 35) has been announcing today that they will be premiering a new Modest Mouse song tomorrow. No time has been mentioned. It's presumed that this will be "The Ground Walks, With Time in a Box", a track which earlier this week had it's run time displayed on iTunes to be 6:10. This may also indicate that the track may be available for purchase or to those that pre-ordered the album next week Tuesday.
Next, the band has also been added to the Open'er Festival in Poland. Modest Mouse were due to perform at the festival in 2013, before that entire European tour was scrapped, so this will now be the band's first performance in that country. The Open'er Festival show is to take place on July 1st. This is good news for the Europeans, as it is the second European festival to announce that Modest Mouse will be performing over there in June/July. However the European dates are also the only ones so far not confirmed on ModestMouse.com.
Lastly: Hastings, a media retailer in the US, has posted track times on their listing for "Strangers to Ourselves". I won't post them all again, you can just see them here, but this would bring the album running time to somewhere in the 57 minute and 10 second area.