OrePolynomial[{{-t^2 + 16*t^4, {3}}, {2*(-3*t + 4*t^2 + 64*t^3), {2}}, 
  {2*(-3 + 14*t + 112*t^2), {1}}, {4*(3 + 16*t), {0}}}, 
 OreAlgebraObject[{Der[t]}, Together, Together[#1 + #2] & , 
  Together[#1*#2] & , None], DegreeLexicographic]
