Greek letters range from 0 to 3, Latin letters from 1 to 3. Subscripts in the Algol68 code are systematically one greater.
∂_γg_αβ:
∂_jg_αβ = 0
∂₀g₀₀ = 2t⁻³
∂_jg_kk = −2t⁻³
∂_jg_kn = 0 if k≠n

Γ^γ_αβ = ½ g^γδ(∂_αg_βδ + ∂_βg_δα − ∂_δg_αβ)
This program computes several quantities for the space. It seems that that
Γ^γ_αβ = (−1/t)IF α=β⋀γ=0 ⋁ β=γ⋀α=0 ⋁ γ=α⋀β=0 THEN 1 ELSE 0 FI
which is a peculiar symmetry.
map:
math Algol 68
g_αβ g[α, β]
g^αβ gu[α, β]
∂_αg_βγ dg[α, β, γ]
Γ^γ_αβ chu[γ, α, β]
∂_δΓ^γ_αβ dchu(δ, γ, α, β)
R^α_βγδ rie[α, β, γ, δ]
R_αβγδ riel[α, β, γ, δ]
R_αβ rie2[α, β]
R rie0
C_αβγδ c[α, β, γ, δ]

R^μ_σαβ = − ∂_βΓ^μ_σα + ∂_αΓ^μ_σβ + Γ^μ_ραΓ^ρ_σβ − Γ^μ_ρβΓ^ρ_σα

Weyl Tensor = (too) = C_abcd = R_abcd
+ (g_adR_cb + g_bcR_ad − g_acR_db − g_bdR_ca)/(4−2)
+ (g_acg_db − g_adg_cb)R/((n−1)(n−2))

I am mystified that the Weyl tensor does not vanish—it is proportional to the Riemann tensor:

R_ijij = 2t⁻⁴ = −R_ijji for i≠0 ⋀ j≠0 ⋀ i≠j,
R_ijkl = 0 otherwise.
C_ijkl = 2R_ijkl

The program is less general that you might think at first glance. It assumes a diagonal metric when it inverts the matrix. (Here is a general matrix inversion routine.) It exploits the fact that g_αβ and Γ^γ_αβ are each proportional to a power of t as it computes their derivative.

R_jk =
0 0 0 0
0 −2t⁻² 0 0
0 0 −2t⁻² 0
0 0 0 −2t⁻²
and thus this metric does not satisfy Einstein’s equations for any cosmological constant except with some matter density.

Square all this with decomposition!
More map:
math Algol 68
S_αβγδ su[α, β, γ, δ]
S_αβ su2[α, β]
E_αβγδ e[α, β, γ, δ]
The two computations of the Weyl tensor agree!

math	Algol 68
S_αβγδ	su[α, β, γ, δ]
S_αβ	su2[α, β]
E_αβγδ	e[α, β, γ, δ]