Ah, a help request related to one of my favourite games - how could I resist? :-)
Here's my attempt:
dropbox.com/s/r9r3moemj140ymf/theWitness.c3p
The line is drawn on the grid, allows backtracking and is blocked by itself and gaps. I've not worked out how to manoeuvre the cursor into the end spot yet - I'll give it some more thought and get back to you.