The generator matrix

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

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+50x^16+64x^17+136x^18+192x^19+157x^20+192x^21+112x^22+64x^23+41x^24+8x^26+7x^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 0.0139 seconds.