The generator matrix

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

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+18x^16+34x^17+84x^18+44x^19+702x^20+16x^21+66x^22+20x^23+15x^24+14x^25+9x^26+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 0.016 seconds.