The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+50x^7+129x^8+178x^9+324x^10+170x^11+110x^12+46x^13+12x^14+4x^15

The gray image is a linear code over GF(2) with n=40, k=10 and d=14.
This code was found by Heurico 1.11 in 6.87e-008 seconds.