  We present a code for numerical simulations of the collapse of regular
initial data to a black hole in null coordinates. We restrict to twist-free
axisymmetry with scalar field matter. Our coordinates are $(u,x,y,\varphi)$,
where the retarded time $u$ labels outgoing null cones emerging from a regular
central worldline, the angles $(\theta,\varphi)$ label the null generators of
each null cone, and the radial coordinate $x$ labels points along these
generators. We focus on a class of generalised Bondi radial coordinates $x$
with the twin properties that $x=0$ is the central world line and that the
numerical domain $(u\ge0$, $0\le x\le x_\text{max})$ is a subset of the domain
of dependence of the initial data on $(u=0$, $0\le x\le x_\text{max}$). In
critical collapse, an appropriate choice of these coordinates can be made to
zoom in on the accumulation point of scale echos of the critical solution,
without the need for explicit mesh refinement. We introduce a novel numerical
scheme that in effect reduces the angular resolution at small radius, such that
the time step $\Delta u$ for an explicit numerical scheme is limited by the
radial resolution $\Delta x$, rather than $\Delta x(\Delta\theta)^2$. We
present convergence tests in the weak-field regime, where we have exact
solutions to the linearised scalar and gravitational-wave equations.
