The generator matrix

 1  1  1  1  1  1  X  X  1  1  1
 0  X  0  0  0  X X^2  0  X  X X^2
 0  0  X  0  0  X  0  X  X X^2  X
 0  0  0  X  0  X X^2 X^2+X X^2 X^2+X X^2+X
 0  0  0  0  X  X X^2+X X^2 X^2  X X^2+X
 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+54x^6+104x^7+139x^8+360x^9+840x^10+1104x^11+807x^12+400x^13+158x^14+72x^15+44x^16+8x^17+4x^18+1x^20

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 0.0276 seconds.