OrePolynomial[{{-t^2 + 7*t^4 - 14*t^6 + 2*t^8 + 15*t^10 - 9*t^12, {3}}, 
  {-t - t^3 + 14*t^5 - 18*t^7 + 51*t^9 - 45*t^11, {2}}, 
  {1 - 3*t^2 - 58*t^4 + 54*t^6 - 39*t^8 + 45*t^10, {1}}, 
  {32*(5*t^3 - 9*t^5 + 6*t^7), {0}}}, OreAlgebraObject[{Der[t]}, Together, 
  Together[#1 + #2] & , Together[#1*#2] & , None], DegreeLexicographic]
