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 X^2+X X+1  1  0  0
 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 X^2 X^2 X^2  0
 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 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 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+85x^8+176x^10+256x^11+1056x^12+1792x^13+1440x^14+1792x^15+1091x^16+256x^17+176x^18+64x^20+7x^24

The gray image is a linear code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.118 seconds.