The generator matrix

 1  0  0  1  1  1  X X^2  1  1 X^2
 0  1  0  1  X X^2+X+1  1  0 X^2+X  1  X
 0  0  1  1  1  0  1  1 X+1  X  0
 0  0  0  X  0 X^2+X X^2  X X^2  0 X^2+X
 0  0  0  0 X^2 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 7.

Homogenous weight enumerator: w(x)=1x^0+70x^7+260x^8+410x^9+898x^10+828x^11+884x^12+420x^13+252x^14+62x^15+7x^16+2x^17+2x^18

The gray image is a linear code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.16 in 0.037 seconds.