The generator matrix

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

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+62x^16+48x^17+192x^18+464x^19+518x^20+464x^21+192x^22+48x^23+54x^24+2x^28+3x^32

The gray image is a linear code over GF(2) with n=160, k=11 and d=64.
This code was found by Heurico 1.16 in 0.031 seconds.