The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X  1  1  1
 0  1  0  0  1 X+1  1 X^2  X  1 X^2+X X^2+X X^2+1
 0  0  1 X+1  1  0  1  X X^2+X X^2 X^2 X^2+1 X+1
 0  0  0 X^2 X^2 X^2  0  0  0 X^2 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+83x^10+112x^11+212x^12+242x^13+194x^14+78x^15+75x^16+14x^17+11x^18+2x^19

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 0.0057 seconds.