The generator matrix

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

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+20x^5+64x^6+44x^7+730x^8+44x^9+64x^10+20x^11+18x^12+1x^16

The gray image is a linear code over GF(2) with n=64, k=10 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.