The generator matrix

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

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+192x^17+677x^18+564x^19+1258x^20+636x^21+566x^22+116x^23+53x^24+20x^25+5x^26+8x^27

The gray image is a linear code over GF(2) with n=160, k=12 and d=68.
This code was found by Heurico 1.16 in 0.078 seconds.