The generator matrix

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

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+91x^10+96x^11+241x^12+192x^13+214x^14+96x^15+77x^16+15x^18+1x^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 0.0102 seconds.