The generator matrix

 1  0  0  0  1  1  1  X  1  1  1
 0  1  0  0  1  X X+1  1  0  1  X
 0  0  1  0  1 X+1  X X^2+1  X X+1  1
 0  0  0  1  X  1 X^2+1  1 X+1 X+1  0

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+76x^7+198x^8+412x^9+960x^10+784x^11+944x^12+480x^13+192x^14+36x^15+9x^16+4x^17

The gray image is a linear code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.11 in 0.015 seconds.