The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X
 0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 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 16.

Homogenous weight enumerator: w(x)=1x^0+210x^16+160x^18+1024x^21+320x^22+280x^24+32x^26+21x^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 1.41 seconds.