The generator matrix

 1  0  1  1  1  0  X  1  1  1  1
 0  1  1  0 X+1  1  X  0 X^2+X  0  0
 0  0  X X^2+X  0 X^2+X  X  0 X^2  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 X^2 X^2  0
 0  0  0  0  0 X^2 X^2 X^2  0  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+44x^6+142x^8+192x^9+320x^10+640x^11+336x^12+192x^13+140x^14+33x^16+8x^18

The gray image is a linear code over GF(2) with n=44, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00638 seconds.