The generator matrix

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

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+467x^16+1488x^17+3806x^18+6392x^19+8360x^20+6616x^21+3812x^22+1320x^23+416x^24+56x^25+30x^26+4x^28

The gray image is a linear code over GF(2) with n=160, k=15 and d=64.
This code was found by Heurico 1.16 in 15.8 seconds.