The generator matrix

 1  1  1  1  1  1  X  X  1  1
 0  X  0  0  0  X X^2  0  X  X
 0  0  X  0  X  X  X X^2  X X^2+X
 0  0  0  X  X  0  0  X X^2  X
 0  0  0  0 X^2  0 X^2  0  0 X^2
 0  0  0  0  0 X^2 X^2 X^2  0 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+97x^6+292x^8+256x^9+751x^10+256x^11+308x^12+79x^14+7x^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 0.102 seconds.