The generator matrix

 1  0  0  0  0  1  1  1  1  X  1  0  X  1
 0  1  0  0  0  0  1  1 X^2+1  1  X  X  1  0
 0  0  1  0  0 X+1 X+1  X X^2  1 X^2  1 X+1  0
 0  0  0  1  0  1  X X+1  X X^2+1  1 X+1  0  0
 0  0  0  0  1  1 X^2  0 X+1 X^2+1 X+1  X  1  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2

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+93x^8+494x^9+1347x^10+4204x^11+6471x^12+13650x^13+12879x^14+13864x^15+6438x^16+4210x^17+1321x^18+428x^19+117x^20+14x^21+5x^22

The gray image is a linear code over GF(2) with n=56, k=16 and d=16.
This code was found by Heurico 1.13 in 2.89 seconds.