The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1
 0 X^2  0  0  0  0  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0
 0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  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+78x^16+32x^17+52x^18+704x^21+48x^24+32x^25+72x^26+1x^32+4x^34

The gray image is a linear code over GF(2) with n=84, k=10 and d=32.
This code was found by Heurico 1.16 in 0.022 seconds.