The generator matrix

 1  0  0  0  1  1  1  X  1  1  1
 0  1  0  0  X  1  1  1  X  X  0
 0  0  1  0 X+1  1  X X+1  0  X  X
 0  0  0  1  1 X^2+X X+1  1  1 X+1  1
 0  0  0  0 X^2  0  0 X^2  0 X^2 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 X^2  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+180x^6+288x^7+1874x^8+2688x^9+8188x^10+6336x^11+8184x^12+2688x^13+1868x^14+288x^15+181x^16+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 1.16 in 38.4 seconds.