The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2+X X^2  X  X X^2  X X^2 X^2  0
 0  0  X  0  0  0  X X^2+X  X  X  X  0  X X^2 X^2  0  0 X^2+X  0 X^2 X^2
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2+X X^2+X X^2+X  X X^2+X  X X^2+X  X  0
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X X^2+X  0 X^2 X^2+X  0 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 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+363x^16+120x^18+620x^20+2048x^21+272x^22+483x^24+120x^26+68x^28+1x^40

The gray image is a linear code over GF(2) with n=84, k=12 and d=32.
This code was found by Heurico 1.16 in 98.5 seconds.