The generator matrix

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

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+149x^8+570x^10+1970x^12+2802x^14+1981x^16+590x^18+118x^20+6x^22+5x^24

The gray image is a linear code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.191 seconds.