The generator matrix

 1  1  1  1  X  X  X  X  X  1  1
 0  X  0  X  0  X X^2+X X^2 X^2  X  0
 0  0  X  X  X  X  0  X  X  X  0
 0  0  0 X^2  0  0 X^2 X^2  0  0  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  0  0 X^2 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+7x^6+40x^7+42x^8+156x^9+83x^10+376x^11+72x^12+160x^13+37x^14+32x^15+13x^16+4x^17+1x^18

The gray image is a linear code over GF(2) with n=44, k=10 and d=12.
This code was found by Heurico 1.16 in 0.00288 seconds.