The generator matrix

 1  1  1  1  1  X  X  X  1  1  1  X  X  X
 0  X  0  X  0  0  X  X X^2  X  0 X^2+X X^2 X^2
 0  0  X  X  0  X  X  0  X  X X^2  0  X  X
 0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  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+47x^8+16x^9+254x^10+144x^11+566x^12+352x^13+1318x^14+352x^15+613x^16+144x^17+218x^18+16x^19+50x^20+2x^22+3x^24

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 0.0462 seconds.