The generator matrix

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

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+37x^6+52x^7+149x^8+268x^9+437x^10+1188x^11+1392x^12+2588x^13+4162x^14+2588x^15+1379x^16+1188x^17+458x^18+268x^19+144x^20+52x^21+25x^22+7x^24+1x^26

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 0.456 seconds.