The school apparently has no catchment area as such but selects on exam pass, whether the school was placed 1st, SEN, brother or sister attending and finally distance.
It is illegal under the DCSF Admissions Code for the school to select children on the basis of where the school is ranked on the CAF.
These are the specific over-subscription criteria for Lincolnshire schools. Obviously a pass of 220 is the first criterion for admission to a grammar school, and then places are allocated in this order:
A. The child is in the care of the local authority.
B. There is a brother or sister at the school who will still be attending
when the child is due to start.
C. The child meets the religious criteria for Stickney William Lovell Church
of England School given below.
D. The distance from the home to the school. Priority will be given to the
child living nearest the school, as defined in note 4.
I can't immediately find the Lincolnshire parent information pack for school applications, but I am certain that there will have been a specific deadline for providing evidence of your address for the purposes of determining where you live, so moving house now will not help.
I suggest that you call Lincs Admissions to ask them what the allocation distances for the school have been in previous years.