The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+236x^16+240x^18+406x^20+80x^22+58x^24+2x^28+1x^32

The gray image is a linear code over GF(2) with n=76, k=10 and d=32.
This code was found by Heurico 1.16 in 46.2 seconds.