The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+40x^17+14x^18+16x^19+14x^20+40x^21+1x^22+1x^24+1x^30

The gray image is a linear code over GF(2) with n=76, k=7 and d=34.
This code was found by Heurico 1.16 in 0.0478 seconds.