The generator matrix

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

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+94x^8+236x^9+604x^10+1928x^11+3460x^12+7028x^13+6036x^14+7088x^15+3417x^16+1940x^17+644x^18+200x^19+68x^20+12x^21+12x^22

The gray image is a linear code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 2.67 seconds.