The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1x^20+10x^21+2x^22+2x^23

The gray image is a linear code over GF(2) with n=80, k=4 and d=40.
This code was found by Heurico 1.16 in 0.00147 seconds.