The generator matrix

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

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+28x^6+77x^8+112x^10+424x^12+2792x^14+459x^16+112x^18+56x^20+28x^22+7x^24

The gray image is a linear code over GF(2) with n=56, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0327 seconds.