The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1  1  X  0  1 X^2+X  1  1  1  1  1  1
 0  1  1 X^2+X X^2+X+1  1 X^2  1 X+1  X X^2+1  1  1 X^2+X  1 X^2+X+1  0  1 X^2+X  1 X^2+X+1
 0  0  X  0 X^2+X X^2  X  X  0 X^2+X  0  X X^2  0 X^2 X^2+X X^2 X^2+X  0  X  0
 0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  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+38x^17+108x^18+98x^19+218x^20+124x^21+205x^22+88x^23+97x^24+26x^25+6x^26+6x^27+4x^28+4x^29+1x^30

The gray image is a linear code over GF(2) with n=84, k=10 and d=34.
This code was found by Heurico 1.16 in 0.0153 seconds.