The generator matrix

 1  0  0  1  1  1 X^3+X X^3+X^2+X X^3  1  1  1  1 X^3+X^2 X^3+X^2+X  1  1  1  1  1
 0  1  0 X^2 X^2+1  1  1  1 X^3+X^2+X X^3+X^2 X^2+X+1 X^3+1 X^3+X  1 X^2 X^2+X X^3+X+1 X+1 X^2+X+1 X^3
 0  0  1 X^2+X+1 X+1 X^2 X^2+1 X^3+X+1  1 X^2+X  X X^3+1 X^2+1 X^3+X^2+1  1 X^3+X^2+X X^3+X+1  0 X^3+1 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+148x^17+549x^18+838x^19+1179x^20+724x^21+405x^22+170x^23+68x^24+4x^25+6x^26+4x^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 0.141 seconds.