The generator matrix

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

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+57x^6+32x^7+333x^8+32x^9+54x^10+2x^12+1x^14

The gray image is a linear code over GF(2) with n=64, k=9 and d=24.
This code was found by Heurico 1.16 in 6.87e-008 seconds.