The generator matrix

 1  0  0  0  1  1  1  1 X^2+X  1  0
 0  1  0  0  1  X X^2+X X+1  1 X^2+X  1
 0  0  1  0  1  0 X+1  0 X+1 X+1  1
 0  0  0  1  1  1  X  X X+1 X+1 X+1
 0  0  0  0  X  0  X X^2+X X^2  0  X
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 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+103x^6+502x^7+1452x^8+3542x^9+7129x^10+7276x^11+7172x^12+3548x^13+1465x^14+478x^15+79x^16+14x^17+7x^18

The gray image is a linear code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.16 in 1.2 seconds.