The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+90x^14+271x^16+144x^17+386x^18+240x^19+478x^20+112x^21+206x^22+16x^23+80x^24+22x^26+2x^28

The gray image is a linear code over GF(2) with n=76, k=11 and d=28.
This code was found by Heurico 1.16 in 0.0526 seconds.