The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  0  0  X  0  X X^2  0
 0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X  0 X^2 X^2  X
 0  0  0  X  X  0  X X^2+X  0  X  X X^2 X^2 X^2+X  X X^2+X  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 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+75x^12+236x^14+64x^15+471x^16+384x^17+440x^18+64x^19+236x^20+60x^22+16x^24+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 0.04 seconds.