The generator matrix

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

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+48x^6+204x^7+358x^8+1080x^9+696x^10+1072x^11+408x^12+200x^13+24x^14+4x^15+1x^16

The gray image is a linear code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.11 in 0.016 seconds.