The generator matrix

 1  0  0  0  0  1  1  1  1  1  0
 0  1  0  0  0  0  1  1  X X^2  1
 0  0  1  0  0 X+1 X+1  X X^2+1  0 X^2+X
 0  0  0  1  0  1  X X+1 X^2+X  X X^2+X+1
 0  0  0  0  1  1 X^2  0 X^2+1 X+1  X
 0  0  0  0  0 X^2  0 X^2 X^2 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+239x^6+888x^7+2968x^8+7480x^9+13209x^10+15984x^11+13100x^12+7600x^13+3025x^14+792x^15+219x^16+24x^17+7x^18

The gray image is a linear code over GF(2) with n=44, k=16 and d=12.
This code was found by Heurico 1.13 in 14.7 seconds.