The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  0  1  1  X  1  1  1  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^3 X^2+X  X X^3+X^2 X^3+X^2 X^3+X^2+X  X X^2+X X^3+X  0 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2  0 X^2  0 X^3 X^2  0 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3
 0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  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 17.

Homogenous weight enumerator: w(x)=1x^0+48x^17+84x^18+220x^19+341x^20+196x^21+84x^22+36x^23+1x^24+12x^25+1x^36

The gray image is a linear code over GF(2) with n=160, k=10 and d=68.
This code was found by Heurico 1.16 in 3.81e-009 seconds.