The generator matrix

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

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+23x^4+48x^5+150x^6+208x^7+1183x^8+208x^9+164x^10+48x^11+9x^12+6x^14

The gray image is a linear code over GF(2) with n=64, k=11 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.