The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+126x^11+84x^12+148x^13+16x^14+96x^15+27x^16+12x^17+2x^19

The gray image is a linear code over GF(2) with n=52, k=9 and d=22.
As d=22 is an upper bound for linear (52,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.11 in 3.81e-009 seconds.