Some people have positive ANA with Hashimoto's, but, typically, that's an indication of another autoimmune, such as RA or Lupus, etc. Have you already been diagnosed with Hashimoto's? Once you have one autoimmune disease, the chances of having another are greater.
My ANA came back as <1:80 and I have Hashimoto's thyroiditis. I have read sensitivity of the ANA for Hashimoto's thyroiditis is 46%. An homogeneous ANA pattern can be seen with Systemic lupus erythematosus, Mixed connective tissue disease, Drug induced lupus, Juvenile idiopathic arthritis.