OrePolynomial[{{9*t^2 - 15*t^4 - 2*t^6 + 14*t^8 - 7*t^10 + t^12, {3}}, 
  {9*t - 39*t^3 - 30*t^5 + 98*t^7 - 43*t^9 + 5*t^11, {2}}, 
  {-81 + 51*t^2 - 102*t^4 + 170*t^6 - 41*t^8 + 3*t^10, {1}}, 
  {32*(6*t - 9*t^3 + 5*t^5), {0}}}, OreAlgebraObject[{Der[t]}, Together, 
  Together[#1 + #2] & , Together[#1*#2] & , None], DegreeLexicographic]
