The generator matrix

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

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+98x^10+80x^11+230x^12+224x^13+220x^14+80x^15+71x^16+18x^18+2x^20

The gray image is a linear code over GF(2) with n=52, k=10 and d=20.
This code was found by Heurico 1.16 in 7.17 seconds.