The generator matrix

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

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+68x^6+294x^8+384x^9+656x^10+1280x^11+672x^12+384x^13+292x^14+57x^16+8x^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 0.0175 seconds.