The generator matrix

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

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+49x^6+256x^7+413x^8+256x^9+46x^10+2x^12+1x^14

The gray image is a linear code over GF(2) with n=64, k=10 and d=24.
This code was found by Heurico 1.16 in 3.62e-008 seconds.