The generator matrix
1 1 1 1 X 1 1 1
0 X 0 X^3+X^2+X X^2+X X^2 X^2+X 0
0 0 X^3+X^2 X^2 X^3 X^2 0 0
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 5.
Homogenous weight enumerator: w(x)=1x^0+14x^5+41x^6+212x^7+493x^8+208x^9+38x^10+12x^11+2x^12+2x^13+1x^14
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 3.81e-009 seconds.