The generator matrix

 1  0  0  0  1  1  1  1 X^2+X  X  1  1  1  1
 0  1  0  0  1  X X^2+X X+1  1  X X^2 X+1 X^2+1  0
 0  0  1  0  1  0 X+1  0 X+1  X X^2  X X^2  0
 0  0  0  1  1  1  X  X X+1  1 X^2+X+1  1 X^2+1  0
 0  0  0  0  X  0  X X^2+X X^2 X^2+X X^2+X X^2  X  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 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+128x^8+268x^9+912x^10+2064x^11+3758x^12+5844x^13+6776x^14+5920x^15+3759x^16+2004x^17+944x^18+272x^19+98x^20+12x^21+8x^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 2.45 seconds.