The generator matrix

 1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0
 0  0 X^3  0  0  0  0  0
 0  0  0 X^3  0  0  0  0
 0  0  0  0 X^3  0  0  0
 0  0  0  0  0 X^3  0  0
 0  0  0  0  0  0 X^3  0
 0  0  0  0  0  0  0 X^3

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+8x^2+28x^4+56x^6+1862x^8+56x^10+28x^12+8x^14+1x^16

The gray image is a linear code over GF(2) with n=64, k=11 and d=8.
This code was found by Heurico 1.16 in 6.87e-008 seconds.