The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+3x^20+16x^21+3x^22+8x^23+1x^26

The gray image is a linear code over GF(2) with n=84, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00177 seconds.