The generator matrix

 1  0  0  1  1  1  X  1  1  1 X^2 X^2+X  1  1  1 X^2 X^2  0  1
 0  1  0  1  X X^2+X+1  1 X^2+X  1 X^2+X+1  0  1  0 X+1 X^2+X+1  1  1  1  0
 0  0  1  1  1  0  1  X X^2+X X^2+1  1  1 X^2+X+1  0  1 X^2+X+1  X X^2+X  0
 0  0  0  X  0 X^2+X X^2 X^2+X  0  X X^2+X  X X^2+X  X X^2  X  0  X  0
 0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 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+76x^14+166x^15+362x^16+424x^17+716x^18+622x^19+727x^20+424x^21+332x^22+138x^23+77x^24+16x^25+12x^26+2x^27+1x^28

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 0.125 seconds.