I agree with all the comments about taking the pressure off as much as possible, rewards for homework, etc but I also think you need to try to get to the bottom of why he can't concentrate in the classroom.
Has anyone looked into his sensory processing? My DD2 has AS and she cannot concentrate in rooms where the smells, lights, touches or noise are overpowering.
The smell could be of washing powder on another child's clothes or the teacher's perfume.
Noises could be from flourescent tubes, other children whispering or a fan running.
The light could simply be the sun being low in the sky and shining in through the window.
Touching could be a label in her clothes, other pupils brushing past her or someone wobbling the table.
They are all things that most children will take in their stride or perhaps find to be a minor irritation but my DD zones out completely. She literally takes herself away from the classroom in her head and becomes unaware of what is happening around her and the passage of time. It is a self defence mechanism and the solution is to remove the sensory stimuli she can't cope with. She doesn't recognise these stimuli as problematic for herself. Someone else has to notice them for her a lot of the time. It took a skilled OT and a specialist Autism teacher to spot what was happening but small adjustments have made a big difference.
She also has always had a big problem with homework. In her head school work is for school and home is for relaxing. In the end the Ed Psych recommended that the school stopped asking her to do it.
Another thing you should look into is Pathological Demand Avoidance (PDA). It is an element of Autism but can be an overarching difficulty on its own. Children with this don't respond well to normal behaviour management strategies and find pressure to do things unbearable and counter-productive. Putting pressure on my DD2 to perform increases her anxiety and reduces her ability to process thought and language. She then has no hope of completing a task.
Another thing to look at is "Impaired Executive Junction". This is another element of Autism but is also present in ADD and ADHD. It can mean that a task which involves several elements can become overwhelming even though each individual element is well within the child's ability. My DD2 freezes when presented with a blank piece of paper yet she can verbally recount all the information she needs to present on the paper faultlessly. She needs a framework to work within.
One of DD2's biggiest issues when writing anything in the classroom is the overwhelming choices of words and methods she has to choose from. She went through a stage of having to do every sum using every method because she couldn't choose just one. Writing things down was nigh on impossible because she had to choose every option for every word and her sentences became lists of similes. Her solution was to zone out and write nothing until a teacher or TA was talking her through it and choosing the words for her. Again it took a lot of hard work to find out what was going on and why.
Despite all of these difficulties DD2 is very academically able and is very adept at appearing to be neurotypical and simply a bit awkward and inattentive.
There are ways that the teachers would help work out if any of these problems are the root cause of his concentration problems. They could also invite their Autism outreach team to come and observe him in the classroom.
I think you need to ask for a meeting with the class teacher and SENCo and start by asking them to give him a homework-free period. In the meantime they can look further into what might be disrupting his attention.