  In this paper we describe an algorithm for generating all the possible
$PIW(m,n,k)$ - integer $m\times n$ Weighing matrices of weight $k$ up to
Hadamard equivalence. Our method is efficient on a personal computer for small
size matrices, up to $m\le n=12$, and $k\le 50$. As a by product we also
improved the \textit{\textbf{nsoks}} \cite{riel2006nsoks} algorithm to find all
possible representations of an integer $k$ as a sum of $n$ integer squares.
  We have implemented our algorithm in \texttt{Sagemath} and as an example we
provide a complete classification for \ $n=m=7$ and $k=25$. Our list of
$IW(7,25)$ can serve as a step towards finding the open classical weighing
matrix $W(35,25)$.
