The generator matrix

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

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+302x^14+608x^15+1303x^16+1800x^17+2616x^18+2816x^19+3022x^20+1936x^21+1176x^22+480x^23+248x^24+40x^25+32x^26+2x^28+2x^30

The gray image is a linear code over GF(2) with n=76, k=14 and d=28.
This code was found by Heurico 1.13 in 31.9 seconds.