The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who�s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+142x^16+198x^18+359x^20+196x^22+97x^24+22x^26+9x^28

The gray image is a linear code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0189 seconds.