OrePolynomial[{{2*t^4 - t^6 - 2*t^8 + t^14, {4}}, 
  {4*(-t^3 - 3*t^5 - 7*t^7 + 6*t^9 + 2*t^11 + 3*t^13), {3}}, 
  {-6*t^2 + 7*t^4 - 10*t^6 + 132*t^8 + 40*t^10 + 29*t^12, {2}}, 
  {5*(6*t + 3*t^3 + 10*t^5 + 12*t^7 + t^11), {1}}, 
  {-5*(6 + 3*t^2 + 10*t^4 + 12*t^6 + t^10), {0}}}, 
 OreAlgebraObject[{Der[t]}, Together, Together[#1 + #2] & , 
  Together[#1*#2] & , None], DegreeLexicographic]
