The generator matrix

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

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+40x^17+131x^18+250x^19+278x^20+166x^21+71x^22+38x^23+25x^24+18x^25+5x^26+1x^30

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 0 seconds.