The generator matrix

 1  0  0  1  1  1 X^3+X  1  1 X^3+X^2  1 X^2+X  1 X^2+X  1  1  1  1  1  1
 0  1  0 X^2  1 X^3+X+1  1 X^3+X X^3+X^2+1  1  0  1 X^3+X+1 X^3  1 X^3+X^2+1 X^3+X X^2+X X^2+1 X^3
 0  0  1 X^2+X+1  1 X^2 X^2+1 X^2+1  X X+1 X^2+X X^2+X X^3+1  1 X^2+X+1 X^3+X+1 X^3+X^2+1 X+1  1 X^3
 0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 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+62x^16+380x^17+937x^18+1414x^19+2653x^20+1428x^21+862x^22+352x^23+73x^24+17x^26+10x^27+3x^28

The gray image is a linear code over GF(2) with n=160, k=13 and d=64.
This code was found by Heurico 1.16 in 0.297 seconds.