The generator matrix

 1  0  0  1  1  1  X  1  1 X^2 X^2  X  1  1  X X^2 X^2 X^2+X  0  X  X
 0  1  0  0  1  1  1  X X^2+X+1  1  1  X  X X^2+X+1  1  1  X  0  1  1 X^2
 0  0  1 X+1 X^2+X+1  0  1  1  X  1  X  1  X X^2+1 X^2+X+1  X  1  1  0  1  X
 0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2
 0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 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+332x^16+128x^17+844x^18+512x^19+1940x^20+768x^21+1772x^22+512x^23+1008x^24+128x^25+196x^26+44x^28+4x^30+3x^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 6.23 seconds.