The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^2  X  1
 0  1 X+1 X^2+X X^2+1  1 X^2  X X^2+X+1  1  1  1  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+6x^12+48x^13+6x^14+1x^16+2x^18

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 0.000352 seconds.