The generator matrix

 1  0  0  1  1  1  0 X^2  1 X^2+X  1  1  1  X  1  1  1  1  1
 0  1  0  0 X^2+1 X^2+1  1  X X^2  1  X X^2+X+1 X^2  1 X+1  0  X X^2 X^2+X
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  0 X^2+X+1  1  X X^2+X+1 X^2  1 X^2+X X^2+X+1  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 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+101x^16+188x^17+162x^18+192x^19+152x^20+88x^21+76x^22+32x^23+18x^24+12x^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 1.16 in 0.0111 seconds.