The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+53x^4+48x^6+842x^8+2208x^10+842x^12+48x^14+53x^16+1x^20

The gray image is a linear code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0172 seconds.