The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^4+966x^8+28x^12+1x^16

The gray image is a linear code over GF(2) with n=64, k=10 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.