The generator matrix

 1  0  1  1  1  0  1  1  0  X  0
 0  1  1  0 X+1  1  0 X+1  1 X^2  X
 0  0  X  0  X  0  X  0  X  0 X^2
 0  0  0  X  X X^2+X  X  0  X  X  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2  0
 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+101x^6+80x^7+489x^8+768x^9+1953x^10+1376x^11+1995x^12+768x^13+495x^14+80x^15+74x^16+11x^18+1x^20

The gray image is a linear code over GF(2) with n=44, k=13 and d=12.
This code was found by Heurico 1.16 in 0.156 seconds.