\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =4\,x \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =x \left ( t \right ) -2\,y \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}z \left ( t \right ) =x \left ( t \right ) -4\,y \left ( t \right ) +z \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.009501 (sec), leaf count = 94 \[ \left \{\left \{x(t)\to c_1 e^{4 t},y(t)\to \frac {1}{6} c_1 e^{-2 t} \left (e^{6 t}-1\right )+c_2 e^{-2 t},z(t)\to \frac {1}{9} c_1 e^{-2 t} \left (e^{3 t}+e^{6 t}-2\right )-\frac {4}{3} c_2 e^{-2 t} \left (e^{3 t}-1\right )+c_3 e^t\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 50 \[ \left \{ \left \{ x \left ( t \right ) ={\it \_C3}\,{{\rm e}^{4\,t}},y \left ( t \right ) ={\frac {{\it \_C3}\,{{\rm e}^{4\,t}}}{6}}+{{\rm e}^ {-2\,t}}{\it \_C2},z \left ( t \right ) ={\frac {{\it \_C3}\,{{\rm e}^{4 \,t}}}{9}}+{\it \_C1}\,{{\rm e}^{t}}+{\frac {4\,{{\rm e}^{-2\,t}}{\it \_C2}}{3}} \right \} \right \} \]