The generator matrix

 1  1  1  1  1  1  1  1  X  X  X
 0  X  0  0  0  X X^2+X  X X^2 X^2 X^2
 0  0  X  0  X  X X^2+X  0  0 X^2 X^2
 0  0  0  X  X  0 X^2+X  X  X X^2+X  0
 0  0  0  0 X^2  0  0 X^2  0  0 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2 X^2 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+116x^6+266x^8+256x^9+676x^10+1536x^11+552x^12+256x^13+348x^14+77x^16+12x^18

The gray image is a linear code over GF(2) with n=44, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0246 seconds.