The generator matrix

 1  0  0  1  1  1  X  1  1  1
 0  1  0  1 X^2+X X^2+X+1  1  X  0 X^2+X
 0  0  1  1 X^2+X+1 X^2+X  1  1 X+1 X+1
 0  0  0 X^2  0  0 X^2  0 X^2  0
 0  0  0  0 X^2  0 X^2  0  0 X^2
 0  0  0  0  0 X^2 X^2 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+79x^6+112x^7+526x^8+656x^9+1339x^10+656x^11+552x^12+112x^13+53x^14+9x^16+1x^18

The gray image is a linear code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 0.203 seconds.