The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  X
 0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  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  0  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+77x^8+296x^12+1280x^14+331x^16+56x^20+7x^24

The gray image is a linear code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0124 seconds.