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

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+7x^18+34x^19+47x^20+28x^21+8x^22+2x^23+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 0.00196 seconds.