functions – Plotting using a ListPlot

I am trying to implement a simple Do loop, but the plot is not printing.

Could you point out what is wrong here and how to stop the error from occurring?

With({(Gamma) = 1, k = 1, (Sigma)1 = 1, (Sigma)2 = 1, dt = 0.01, 
  tfinal = 20, v1 = 2, v2 = 5},
 dtsqrt = Sqrt(dt);
 x1 = 0;
 x2 = 0;
 veclist = {{x1, x2}};
 Do(
  w1 = dtsqrt RandomVariate(NormalDistribution(0, 1));
  w2 = dtsqrt RandomVariate(NormalDistribution(0, 1));
  x1 += k x1 - x2 (k + (Gamma)) + dtsqrt w1;
  x2 += k x1 - x2 (k + (Gamma)) + dtsqrt w2;
  AppendTo(veclist, {x1, x2});
  ,
  {t, dt, tfinal, dt});
  ListPlot(veclist, Joined -> True)
  )