The generator matrix

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

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+67x^14+158x^15+259x^16+504x^17+680x^18+762x^19+716x^20+464x^21+272x^22+130x^23+48x^24+24x^25+4x^26+6x^27+1x^30

The gray image is a linear code over GF(2) with n=76, k=12 and d=28.
This code was found by Heurico 1.16 in 0.15 seconds.