For my question, let's say I have the following quotient module as an example, \begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(0001+x+y+xy1+y+z+yz1+x+z+xz1+z1+x000001+x1+y000\right)} \end{align}
where Z2[x,y,z]3 is a polynomial ring in variables x,y,z over field F2. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.