At 12" it is presumably not a walking path? You could cover it with rounded cobbles or flat crazy paving.

Is the strip sloping or does it run across the slope? If it's flatish you could make it a feature with planters / pots. Balance tongue-in-cheek gnomes/ late Christmas decorations / interestingly shaped bottles on it? Hide it with sprawling planting, though that might get in the way of mowing.

I bought a sedum 'mat' from a national company to go ontop of a manhole cover, you could use the same thing for your strip.
I know the literature says it must be sloping for drainage but mine's not !

you could cover it with decorative aggregate like slate chippings or pebbles and put pots on if its not awalk way,but like Beattie says careful at the edges when mowing

You could edge it with 1/2 sleepers and then fill with any of the above mentioned and coloured ground glass or coloured slate? a bird bath or statue may also sit well along it?

you could build a raised pond at the top and a ground level one at the bottem and build a waterfall over it.put plants in one pond at the top and fish in the bottom . it will be lovley and clean .