The generator matrix

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

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+24x^5+60x^6+104x^7+653x^8+104x^9+44x^10+24x^11+10x^12

The gray image is a linear code over GF(2) with n=64, k=10 and d=20.
This code was found by Heurico 1.16 in 0.015 seconds.