The generator matrix

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

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+10x^17+30x^18+44x^19+31x^20+10x^21+1x^22+1x^34

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 0.0017 seconds.