The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+36x^16+106x^17+100x^18+322x^19+266x^20+436x^21+220x^22+308x^23+106x^24+98x^25+28x^26+10x^27+6x^28+4x^30+1x^32

The gray image is a linear code over GF(2) with n=84, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0462 seconds.