The generator matrix

 1  1  1  1  1  X  X  X  1  0  X  X  1  1
 0  X  0  X  0  0  X X^2+X X^2  0 X^2 X^2  0  0
 0  0  X  X  0  X  X  0  X  X  X  X  0  0
 0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 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+34x^8+144x^10+32x^11+349x^12+224x^13+480x^14+224x^15+349x^16+32x^17+144x^18+34x^20+1x^28

The gray image is a linear code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0153 seconds.