The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+8x^18+32x^19+46x^20+32x^21+7x^22+1x^24+1x^38

The gray image is a linear code over GF(2) with n=80, k=7 and d=36.
This code was found by Heurico 1.16 in 0.00249 seconds.