The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1 X^2+X  1  1  1  1  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1 X^2+1  1  X  0  1 X^2+X X^2+X+1 X^2+X+1 X^2+X X+1
 0  0  X  0 X^2+X  0 X^2+X  0  X X^2  X  X X^2  0 X^2 X^2+X X^2+X  0  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 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+99x^14+48x^15+409x^16+384x^17+778x^18+672x^19+780x^20+384x^21+388x^22+48x^23+86x^24+14x^26+4x^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 20.9 seconds.