The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+84x^17+198x^18+276x^19+345x^20+340x^21+284x^22+224x^23+159x^24+84x^25+30x^26+12x^27+7x^28+4x^29

The gray image is a linear code over GF(2) with n=84, k=11 and d=34.
This code was found by Heurico 1.16 in 0.0411 seconds.