The generator matrix
1 1 1 X 1 X 1 1
0 X^3+X^2 0 0 X^2 X^3+X^2 X^3 X^3+X^2
0 0 X^3+X^2 0 X^2 X^2 0 X^3
0 0 0 X^2 X^3 X^2 X^3+X^2 X^3+X^2
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+24x^5+60x^6+104x^7+653x^8+104x^9+44x^10+24x^11+10x^12
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 0.015 seconds.