The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+254x^16+1x^32

The gray image is a linear code over GF(2) with n=128, k=8 and d=64.
As d=64 is an upper bound for linear (128,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 3.81e-009 seconds.