The generator matrix

 1  0  1  1  1  0  1  1  1  1  1  1  0  1
 0  1  1  0  1  1 X^2+X+1 X^2  0 X+1 X^2+X X^2+1  1  0
 0  0  X  0  0  0  X X^2 X^2+X X^2+X X^2 X^2  0  0
 0  0  0  X  0 X^2+X  X X^2  X X^2 X^2+X X^2 X^2+X  0
 0  0  0  0  X  0 X^2+X  X X^2 X^2+X X^2+X X^2 X^2+X  0
 0  0  0  0  0 X^2 X^2 X^2  0  0 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+51x^8+74x^9+231x^10+396x^11+939x^12+1554x^13+1641x^14+1624x^15+964x^16+382x^17+225x^18+60x^19+29x^20+6x^21+15x^22

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 0.253 seconds.