The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+108x^6+504x^7+1210x^8+4648x^9+4780x^10+10160x^11+4936x^12+4688x^13+1124x^14+472x^15+125x^16+8x^17+4x^18

The gray image is a linear code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.13 in 0.453 seconds.