The generator matrix

 1  1  1  1  1  1  1  1  X  0  X  0 X^2
 0  X  0 X^2+X X^2 X^2+X X^2  X X^2+X  X X^2+X  X  0
 0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+36x^12+16x^14+11x^16

The gray image is a linear code over GF(2) with n=52, k=6 and d=24.
As d=25 is an upper bound for linear (52,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.000663 seconds.