The generator matrix

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

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+60x^17+273x^18+256x^19+298x^20+284x^21+350x^22+232x^23+189x^24+52x^25+33x^26+8x^27+8x^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 0.0419 seconds.