The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1  0  X  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X+1  1  0  0
 0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0  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+46x^8+16x^9+113x^10+272x^11+236x^12+1248x^13+236x^14+1248x^15+217x^16+272x^17+150x^18+16x^19+12x^20+12x^22+1x^26

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 0.0305 seconds.