The generator matrix

 1  0  0  0  0  1  1  1  1 X^2+X  1  1  1  1
 0  1  0  0  0  0 X^2+1 X+1 X^2+1  1  X X^2+X X+1 X+1
 0  0  1  0  0  1  1  X  0  1  0 X^2 X^2+X X^2+X
 0  0  0  1  0  1 X^2  0 X+1 X+1 X+1 X^2+X X^2+X+1 X^2+X
 0  0  0  0  1  1 X^2+X  1  X X+1  X X^2+X+1 X+1 X+1
 0  0  0  0  0  X  0 X^2 X^2+X  X X^2  X X^2  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+251x^8+834x^9+2813x^10+7492x^11+15631x^12+24430x^13+28133x^14+24440x^15+15646x^16+7550x^17+2831x^18+772x^19+213x^20+18x^21+15x^22+2x^24

The gray image is a linear code over GF(2) with n=56, k=17 and d=16.
This code was found by Heurico 1.13 in 11.1 seconds.