OrePolynomial[{{2*t - 121*t^2 - 475*t^3 + 1746*t^4 - 1152*t^5, {3}}, 
  {4 - 514*t - 813*t^2 + 6372*t^3 - 4608*t^4, {2}}, 
  {-4*(74 - 108*t - 801*t^2 + 576*t^3), {1}}}, 
 OreAlgebraObject[{Der[t]}, Together, Together[#1 + #2] & , 
  Together[#1*#2] & , None], DegreeLexicographic]
