The generator matrix

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

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+208x^16+276x^17+752x^18+892x^19+1268x^20+1224x^21+1514x^22+952x^23+666x^24+228x^25+164x^26+12x^27+32x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=84, k=13 and d=32.
This code was found by Heurico 1.16 in 1.72 seconds.