The generator matrix

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

generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+39x^6+32x^7+46x^8+96x^9+75x^10+96x^11+72x^12+32x^13+13x^14+9x^16+1x^18

The gray image is a linear code over GF(2) with n=20, k=9 and d=6.
This code was found by Heurico 1.16 in -1.01e-007 seconds.