The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+63x^4+56x^6+509x^8+288x^10+3011x^12+8528x^14+3011x^16+288x^18+509x^20+56x^22+63x^24+1x^28

The gray image is a linear code over GF(2) with n=56, k=14 and d=8.
This code was found by Heurico 1.16 in 0.275 seconds.