The generator matrix

 1  0  0  1  1  1 X^2  1  1  1 X^2+X  1  0 X^2 X^2 X^2+X  X  X X^2
 0  1  0  1  X X^2+X+1  1  0 X^2+X X^2+1  1  1  1  1  0  1  1 X^2+X  1
 0  0  1  1  1  0 X+1  X X^2+X+1 X+1  0 X^2+X  1  0  1  1 X^2  1  0
 0  0  0  X  0 X^2+X  X X^2+X X^2+X X^2  0 X^2 X^2+X  X  X X^2 X^2+X X^2 X^2+X
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 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+182x^14+160x^15+815x^16+768x^17+1546x^18+1216x^19+1615x^20+768x^21+762x^22+160x^23+192x^24+6x^26+1x^36

The gray image is a linear code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.16 in 4.87 seconds.