The generator matrix

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

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+154x^16+64x^18+1612x^20+64x^22+148x^24+4x^28+1x^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.