The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+87x^12+266x^14+687x^16+638x^18+296x^20+54x^22+16x^24+2x^26+1x^28

The gray image is a linear code over GF(2) with n=68, k=11 and d=24.
This code was found by Heurico 1.16 in 0.147 seconds.