The generator matrix

 1  0  0  1  1  1  X X^2  1  1
 0  1  0  1  X X^2+X+1  1  0 X^2+X X^2
 0  0  1  1  1  0  1  1 X+1  0
 0  0  0  X  0 X^2+X X^2  X X^2  X
 0  0  0  0 X^2 X^2 X^2 X^2  0  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+64x^6+96x^7+610x^8+672x^9+1216x^10+672x^11+600x^12+96x^13+64x^14+5x^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 1.16 in 0.0246 seconds.