The generator matrix

 1  1  1  1 X^3  1 X^3+X^2  1
 0  X  0  X  X X^3+X^2  X X^3
 0  0  X  X X^2  0 X^2+X X^2
 0  0  0 X^3  0 X^3 X^3 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+26x^5+153x^6+360x^7+973x^8+356x^9+150x^10+24x^11+2x^12+2x^13+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 3.62e-008 seconds.