The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+13x^10+40x^11+51x^12+48x^13+49x^14+40x^15+11x^16+1x^18+1x^20+1x^22

The gray image is a linear code over GF(2) with n=52, k=8 and d=20.
This code was found by Heurico 1.16 in 0.00112 seconds.