The generator matrix

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

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+85x^8+140x^10+64x^11+552x^12+1088x^13+768x^14+4992x^15+955x^16+4992x^17+888x^18+1088x^19+440x^20+64x^21+224x^22+15x^24+28x^26

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 0.445 seconds.