The generator matrix

 1  0  1  1  1 X^2  1  1 X^2  1
 0  1  1  0 X+1  1 X+1  0  1  0
 0  0  X  0  0 X^2  X X^2+X  X  0
 0  0  0  X  0 X^2+X  X  X X^2  0
 0  0  0  0 X^2  0  0 X^2 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+36x^6+80x^7+195x^8+432x^9+549x^10+432x^11+218x^12+80x^13+22x^14+2x^16+1x^18

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 0.00784 seconds.