The generator matrix

 1  0  1  1  1  0  0  1
 0  1 X+1 X^3+X^2+X X^2+1  1  1  0
 0  0 X^2 X^2  0  0 X^3  0
 0  0  0 X^3  0 X^3 X^3  0
 0  0  0  0 X^3 X^3  0  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+12x^4+90x^5+203x^6+680x^7+2125x^8+676x^9+210x^10+88x^11+6x^12+2x^13+3x^14

The gray image is a linear code over GF(2) with n=64, k=12 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.