The generator matrix

 1  1  1  1  X  1  1  X
 0  X  0  X X^2 X^2+X  0 X^3+X^2+X
 0  0  X  X  X X^2+X X^2  0
 0  0  0 X^2  0 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+88x^5+204x^6+872x^7+1773x^8+872x^9+188x^10+88x^11+10x^12

The gray image is a linear code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.266 seconds.