The generator matrix

 1  1  1  1  X  1  1  0  X  1  1  X  1  1
 0  X  0 X^2+X  X  0 X^2+X  X  X  0 X^2+X X^2+X X^2+X X^2+X
 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 X^2 X^2  0  0 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  0 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0  0 X^2 X^2  0 X^2 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+85x^8+112x^10+128x^11+544x^12+896x^13+544x^14+896x^15+579x^16+128x^17+112x^18+64x^20+7x^24

The gray image is a linear code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0472 seconds.