The generator matrix

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

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+942x^16+2724x^17+7058x^18+13768x^19+16298x^20+14144x^21+7250x^22+2392x^23+811x^24+124x^25+18x^26+4x^28+2x^30

The gray image is a linear code over GF(2) with n=160, k=16 and d=64.
This code was found by Heurico 1.16 in 270 seconds.