The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1  1 X^2  1  0 X^2  1  X  1  1
 0  1  1  0 X^2+X+1  1  X  1 X+1 X^2 X^2+X+1  1 X^2+1  1  1  1  1 X^2 X+1
 0  0  X  0 X^2+X  0  0 X^2  X X^2+X  0  X  0  X X^2 X^2 X^2+X  X  0
 0  0  0  X  0  0 X^2+X X^2+X  X X^2  X X^2  0 X^2+X  X X^2+X  0 X^2  0
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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+95x^14+80x^15+368x^16+384x^17+812x^18+608x^19+845x^20+384x^21+332x^22+80x^23+95x^24+8x^26+3x^28+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 0.152 seconds.