The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  X  1  0  X  1
 0  1  0  0  0  1  1  1  X  X  0  1  1 X+1  0  1  0
 0  0  1  0  1  1  0  1  0  1  1 X+1  X  0  X  1  0
 0  0  0  1  1  0  1  1  1  0  1  0 X+1  0  1  X  0
 0  0  0  0  X  0  0  0  0  X  0  X  X  X  X  0  0
 0  0  0  0  0  X  0  0  X  X  X  0  X  X  X  0  0
 0  0  0  0  0  0  X  0  X  0  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  X  X  0  X  X  X  0  0  X  X

generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+44x^10+70x^11+131x^12+222x^13+382x^14+422x^15+479x^16+590x^17+454x^18+482x^19+372x^20+202x^21+138x^22+50x^23+40x^24+10x^25+6x^26+1x^28

The gray image is a linear code over GF(2) with n=34, k=12 and d=10.
This code was found by Heurico 1.16 in 0.171 seconds.