P<a,b,c,d,e,f,g,h,i,j,k,l,m,n> := PolynomialRing(IntegerRing(),14);

quadrics := [h*l-i*j,
m*c-n*a,
d*k-e*j,
b*f-g*a,
a*d+a*j+d*i-b*c-b*h-c*l,
j*f+j*a+f*n-h*k-h*m-k*c,
a*l+a*j+l*e-m*b-m*d-b*k,
j*c+j*a+c*g-d*h-d*f-h*b,
a*k+a*j+k*i-f*m-f*l-m*h,
j*b+j*a+b*n-l*d-l*c-d*m,
a*h+a*j+h*e-c*f-c*k-f*d,
j*m+j*a+m*g-k*l-k*b-l*f,
a*j+b*h+b*j-c*g+d*f+d*h+d*j+d*k+f*j-g*n+h*j+h*l+j*j+j*k+j*l+j*m,
j*a+h*m+h*a-k*i+f*l+f*m+f*a+f*b+l*a-i*e+m*a+m*c+a*a+a*b+a*c+a*d];

I := ideal<P | quadrics>;

simples := [a*g-b*f,
j*i-h*l,
a*n-m*c,
j*e-d*k,
(a+c)*(g+j)-(b+d)*(f+h),
(j+k)*(i+a)-(h+f)*(l+m),
(a+b)*(n+j)-(m+l)*(c+d),
(j+h)*(e+a)-(d+c)*(k+f),
(a+m)*(g+j)-(f+k)*(b+l),
(j+d)*(i+a)-(l+b)*(h+c),
(a+f)*(n+j)-(c+h)*(m+k),
(j+l)*(e+a)-(k+m)*(d+b),
c*(f+g+j+k)-h*(a+b+e+d),
k*(l+i+a+b)-m*(j+h+g+f),
b*(c+n+j+h)-d*(a+m+i+l),
h*(k+e+a+m)-f*(j+d+n+c),
m*(b+g+j+d)-l*(a+f+e+k),
d*(h+i+a+f)-c*(j+l+g+b),
f*(m+n+j+l)-k*(a+c+i+h),
l*(d+e+a+c)-b*(j+k+n+m),
a*(a+b+c+d+f+g+h+2*j+l+k+m+n)-e*i,
j*(j+h+k+f+l+i+m+2*a+c+b+d+e)-g*n,
(a+c)*(a+b+f+g+j+k+l+m)-(d+e)*(h+i),
(j+k)*(j+h+l+i+a+b+c+d)-(f+g)*(m+n),
(a+b)*(a+m+c+n+j+h+k+f)-(l+i)*(d+e),
(j+h)*(j+d+k+e+a+m+b+l)-(c+n)*(f+g),
(a+m)*(a+f+b+g+j+d+h+c)-(k+e)*(l+i),
(j+d)*(j+l+h+i+a+f+m+k)-(b+g)*(c+n),
(a+f)*(a+c+m+n+j+l+d+b)-(h+i)*(k+e),
(j+l)*(j+k+d+e+a+c+f+h)-(m+n)*(b+g),
(a+b+c+d)*(f+k+a+m)-e*(h+j+i+l),
(j+h+k+f)*(l+b+j+d)-g*(m+a+n+c),
(a+m+b+l)*(c+h+a+f)-i*(d+j+e+k),
(j+d+h+c)*(k+m+j+l)-n*(f+a+g+b),
(a+b+f+g)*(a+c+m+n)-(d+e+j+k)*(h+i+j+l)];

J := ideal<P | simples>;

I eq J;