The generator matrix

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

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+28x^5+81x^6+388x^7+1053x^8+388x^9+78x^10+28x^11+2x^12+1x^14

The gray image is a linear code over GF(2) with n=64, k=11 and d=20.
This code was found by Heurico 1.16 in -3.24e-008 seconds.