The generator matrix

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

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+99x^16+196x^17+154x^18+180x^19+180x^20+84x^21+52x^22+44x^23+24x^24+8x^25+2x^26

The gray image is a linear code over GF(2) with n=76, k=10 and d=32.
This code was found by Heurico 1.11 in 0 seconds.