The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  X  1  1 X^2+X  1  1 X^3+X^2  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X X^2+X+1  1  X X+1  1 X^3+X^2 X^3+1  1 X^2+X X^3+X^2+1 X+1 X^3+X^2+1  1
 0  0 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3  0 X^3 X^2  0 X^2 X^3+X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+82x^17+192x^18+660x^19+195x^20+652x^21+181x^22+72x^23+3x^24+2x^25+2x^26+4x^27+1x^28+1x^30

The gray image is a linear code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.015 seconds.