Computing the successive minima of the following lattice in $\mathbb{R}^4$

Question

Let us define the lattice $\Lambda$ in $\mathbb{R}^4$ defined by the matrix $$ \Lambda = \begin{bmatrix} A & 0 & 0 & 0 \\ 0 & A & 0 & 0 \\ \gamma_1 & \gamma_2 & B & 0 \\ \gamma_{2} & \gamma_{3} & 0 & B \end{bmatrix}, $$ where all the entries are real numbers. I was wondering is it possible to compute the successive minima just knowing that the lattice has this shape? Any comments/references/suggestions would be appreciated!