The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+44x^8+44x^9+173x^10+288x^11+462x^12+684x^13+684x^14+704x^15+475x^16+292x^17+162x^18+32x^19+42x^20+4x^21+4x^22+1x^26

The gray image is a linear code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0386 seconds.