The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+50x^16+160x^17+40x^18+4x^20+1x^32

The gray image is a linear code over GF(2) with n=136, k=8 and d=64.
As d=66 is an upper bound for linear (136,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 0 seconds.