Does anyone know the 135.008 reference?

I came across this recently and think it could be a nice looking "boys" watch at 32mm without the crown. The dial looks good and original. I can, however, not find any information on the 135.008 reference on this forum or google. The fact that its a De Ville would indicate that it is post 1967. A thing that bothers me is also that the reference is engraved on the outside of the case - I haven't seen this on any (legit) Omegas before personally. Does anyone have any information?

It looks smaller than 32mm.I think a 161.009 or 162.009 with 500 movements at 33mm or any 30mm omega would be much better and safer option .Btw how much they asking?