The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X^3 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0
0 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0
0 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0
0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0
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+15x^16+224x^17+15x^18+1x^34
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 1.05e-007 seconds.