The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  X X^2  1  1  1  X  1  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^2+X  X X^2+X  X X^3+X^2+X  X X^3 X^3+X  X X^2+X  0 X^3+X^2+X
 0  0 X^3+X^2  0 X^2  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3  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+112x^16+160x^17+556x^18+608x^19+1259x^20+608x^21+512x^22+160x^23+91x^24+20x^26+9x^28

The gray image is a linear code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.078 seconds.