The generator matrix

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

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+106x^18+64x^19+188x^20+64x^21+76x^22+2x^24+10x^26+1x^32

The gray image is a linear code over GF(2) with n=160, k=9 and d=72.
This code was found by Heurico 1.16 in 0.157 seconds.