The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+212x^12+624x^14+256x^15+1720x^16+1024x^17+3488x^18+1536x^19+3768x^20+1024x^21+1648x^22+256x^23+660x^24+128x^26+36x^28+3x^32

The gray image is a linear code over GF(2) with n=76, k=14 and d=24.
This code was found by Heurico 1.16 in 2.05 seconds.