Looks like a nice 8x60 to me. The 156,14 is the pre-1912 "gauge" mark which was the only indication of bore size required by the German proof law of 1891. 156,14 gauge translates to .310", so the lamd-to-land diameter of the barrel would have been between .310" and .319", .320" being the next size up of 141,95.

The best thing about this rifle is the very explicit bore, groove and twist rate mark of 7,85 8,15 240 all expressed in mm along with the 8x60 chambering mark. My guess is that this rifle was originally an 8x57J built before 1912 then rechambered and remarked after WWI to 8x60J. Rifles chambered in 8x57 were prohibited for a time after WWI and so some bright light there in Germany came up with the 8x60 after the war as a simple rechamber job to 'legalize' existing rifles. It's also a dandy round in its own right although brass is not nearly as easy to find anymore.