The generator matrix

 1  0  1  1  1  0  X  1
 0  1  1  0  1  1  0  0
 0  0  X  0  0  0  X  0
 0  0  0  X  0  0  X  0
 0  0  0  0  X  0  X  0
 0  0  0  0  0  X  X  0

generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+23x^4+16x^5+22x^6+48x^7+31x^8+48x^9+36x^10+16x^11+9x^12+6x^14

The gray image is a linear code over GF(2) with n=16, k=8 and d=4.
This code was found by Heurico 1.16 in 2.67e-008 seconds.