The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  X  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^3 X^2+X X^3+X^2+X X^3+X^2 X^2+X X^2+X  0
 0  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0
 0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 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+24x^16+68x^17+21x^18+256x^19+299x^20+248x^21+8x^22+64x^23+27x^24+4x^25+2x^26+1x^28+1x^34

The gray image is a linear code over GF(2) with n=160, k=10 and d=64.
This code was found by Heurico 1.16 in 1.05e-007 seconds.