The generator matrix

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

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+201x^18+192x^19+251x^20+192x^21+176x^22+3x^24+6x^26+1x^28+1x^34

The gray image is a linear code over GF(2) with n=160, k=10 and d=72.
This code was found by Heurico 1.16 in 1.09 seconds.