The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  X  1  1
 0  X  0  0  0  0  0  0 X^2 X^2+X X^2+X X^2+X X^2 X^2
 0  0  X  0  0  0  X X^2+X X^2+X  X X^2+X  X  X  0
 0  0  0  X  0  X  X X^2+X  0  0 X^2 X^2+X  0  X
 0  0  0  0  X  X  0 X^2+X  X  X  X X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 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+262x^8+740x^10+2336x^12+2048x^13+5572x^14+2048x^15+2413x^16+716x^18+232x^20+12x^22+4x^24

The gray image is a linear code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 1.3 seconds.