The generator matrix

 1  1  1  1  1  1  1  X  1  0  X  0  X  1
 0  X  0  0  0  0 X^2 X^2+X  X  X X^2  0  0  0
 0  0  X  0  0  0 X^2+X  X X^2  X  0 X^2  0  0
 0  0  0  X  0  X  X X^2  X X^2  X  X  0  0
 0  0  0  0  X  X X^2  X X^2  X X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2  0  0  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+64x^8+68x^9+134x^10+158x^11+700x^12+268x^13+1262x^14+310x^15+725x^16+172x^17+130x^18+42x^19+44x^20+4x^21+10x^22+2x^23+2x^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 0.07 seconds.