The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  1  1  0  X
 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  0 X^2+X X^3+X^2 X^3+X X+1 X^2+1  X X^2+X
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  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+95x^16+96x^17+598x^18+608x^19+1296x^20+544x^21+740x^22+32x^23+76x^24+6x^26+4x^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 0.062 seconds.