The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+40x^6+173x^8+96x^9+448x^10+608x^11+2376x^12+1344x^13+6192x^14+1344x^15+2411x^16+608x^17+448x^18+96x^19+152x^20+40x^22+7x^24

The gray image is a linear code over GF(2) with n=56, k=14 and d=12.
This code was found by Heurico 1.16 in 0.415 seconds.