The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+40x^6+160x^7+194x^8+256x^9+560x^10+576x^11+184x^12+40x^14+32x^15+5x^16

The gray image is a linear code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0105 seconds.