The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X X^2  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  0  X  X  0
 0  0  X  0  X  X X^2+X  0  0 X^2  X  0  X  0
 0  0  0  X  X  0 X^2+X  X  X X^2+X  X  X X^2  0
 0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2  0  0  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+59x^8+60x^9+119x^10+344x^11+213x^12+1100x^13+251x^14+1200x^15+192x^16+308x^17+133x^18+56x^19+47x^20+4x^21+9x^22

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 0.0516 seconds.