The generator matrix

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

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+54x^6+124x^7+404x^8+920x^9+1576x^10+1992x^11+1612x^12+960x^13+406x^14+92x^15+31x^16+8x^17+12x^18

The gray image is a linear code over GF(2) with n=44, k=13 and d=12.
This code was found by Heurico 1.16 in 0.114 seconds.