The generator matrix

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

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+148x^8+64x^10+928x^12+512x^13+1472x^14+3584x^15+2966x^16+3584x^17+1472x^18+512x^19+928x^20+64x^22+148x^24+1x^32

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 13.2 seconds.