The generator matrix

 1  0  0  1  1  1  0  1  X  1 X^2+X  1  1  X  X  X  0  1  1  1
 0  1  0  0  1  1  1 X+1 X^2+X X^2+X  1  X X^2+X+1  1  X X^2  1 X^2+X+1  1 X+1
 0  0  1  1  0 X+1  1 X^2  1  1  X  0 X^2+X+1 X+1  1  1 X^2+1 X^2+X+1 X+1  1
 0  0  0  X X^2 X^2+X  X X^2  X  0  X  X  0  0  0 X^2 X^2  X  X 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+67x^16+222x^17+258x^18+370x^19+275x^20+352x^21+204x^22+184x^23+78x^24+18x^25+10x^26+6x^27+3x^28

The gray image is a linear code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.11 in 0.032 seconds.