The way you propose to simulate $M:=\max_{0 \le t \le 1} |W(t)|$ is very inefficient. The convergence of the discretized version (say $M_N$) of $M$ to $M$ will be very slow, probably at the rate of $1/\sqrt N$ or so, and then you will have to simulate a very large number $N$ of normal random variables -- just to get one realization of $M$. 

A much more efficient way is to use the following explicit expression for the cdf of $M$: 
\begin{equation}
	P(M\le x)=\frac4\pi\, \sum _{k=0}^{\infty } \frac{(-1)^k}{2 k+1}\,
	 \exp \left(-\frac{(2 k+1)^2 \pi ^2}{8
   x^2}\right) \tag{1}
\end{equation}
for $x>0$; see e.g. [page 3][1]. The series in (1) converges very fast unless $x$ is very large. On the other hand, if $x$ is large, then $P(M\le x)$ is very close to $1$. 

More specifically, if $x>x_0=5.8471\ldots$, where $x_0$ is the root of the equation $4(1-\Phi(x_0))=1/10^8$ and $\Phi$ is the standard normal cdf, then, by another formula on the same [page 3][1], 
\begin{equation}
	0<1-P(M\le x)=P(M>x)\le P(M^+>x)+P(M^->x)=2P(M^+>x)=4(1-\Phi(x))<1/10^8, 
\end{equation}
where $M^\pm:=\max_{0\le t\le1}(\pm W(t))$. 
On the other hand, for $x\in(0,x_0]$, retaining only the first $11$ summands of the alternating series in (1), we will get the approximation 
\begin{equation}
	P(M\le x)\approx F(x):=\frac4\pi\, \sum _{k=0}^{10} \frac{(-1)^k}{2 k+1}\,
	 \exp \left(-\frac{(2 k+1)^2 \pi ^2}{8
   x^2}\right) \tag{1}
\end{equation} 
with an error less in absolute value than 
\begin{equation}
	\frac4\pi\,\frac1{2\times11+1}\,
	 \exp \Big(-\frac{(2\times11+1)^2 \pi ^2}{8x_0^2}\Big)<3/10^{10}. 
\end{equation}

Now we can very close approximations $m_1,m_2,\dots$ to iid realizations of $M$ as solutions of the equations $F(m_i)=u_i$, where $u_1,u_2,\dots$ are iid realizations of a random variable uniformy distributed between $0$ and $1$. It then takes under a second in Mathematica to simulate $1000$ very close approximations $m_1,m_2,\dots$ to iid realizations of $M$: 

[![enter image description here][2]][2]
 
 


  [1]: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=2ahUKEwiw1J6e0YzfAhUvpoMKHYS0AgAQFjABegQICBAC&url=https%3A%2F%2Fhal.archives-ouvertes.fr%2Fhal-00784874%2Fdocument&usg=AOvVaw3_r2r6_d0ZpYw9_EWrgNl_
  [2]: https://i.sstatic.net/zI3oE.png