The generator matrix
1 0 0 0 1 1 1 1 1 X 1
0 1 0 0 1 X X X^2+1 0 0 X^2
0 0 1 0 1 0 X^2+1 1 X+1 1 X^2
0 0 0 1 1 X+1 0 1 1 X+1 0
0 0 0 0 X X X^2+X X^2 X^2+X X^2+X 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+47x^6+264x^7+696x^8+1892x^9+3301x^10+3856x^11+3468x^12+1960x^13+617x^14+200x^15+59x^16+20x^17+3x^18
The gray image is a linear code over GF(2) with n=44, k=14 and d=12.
This code was found by Heurico 1.13 in 0.141 seconds.