The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  X  1
 0  1  0  1  0 X^2+X+1  1  1  1  0  0
 0  0  1  1  1  0  1 X^2+X  1  1  0
 0  0  0  X  0 X^2  0 X^2+X  X X^2  0
 0  0  0  0  X  X X^2+X X^2  X X^2+X 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+33x^6+112x^7+318x^8+1000x^9+1689x^10+1856x^11+1720x^12+1040x^13+291x^14+80x^15+41x^16+8x^17+3x^18

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 0.126 seconds.