The generator matrix

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

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+26x^8+32x^9+48x^10+128x^11+165x^12+608x^13+32x^14+608x^15+165x^16+128x^17+48x^18+32x^19+26x^20+1x^28

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 0.0103 seconds.