The generator matrix

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

generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+71x^8+176x^10+288x^11+694x^12+1184x^13+1616x^14+2624x^15+3071x^16+2624x^17+1616x^18+1184x^19+708x^20+288x^21+176x^22+57x^24+6x^28

The gray image is a linear code over GF(2) with n=64, k=14 and d=16.
This code was found by Heurico 1.16 in 0.491 seconds.