The generator matrix

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

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+238x^15+1644x^16+5296x^17+14194x^18+26900x^19+34250x^20+27240x^21+14473x^22+5022x^23+1445x^24+312x^25+36x^26+16x^27+4x^28+1x^30

The gray image is a linear code over GF(2) with n=160, k=17 and d=60.
This code was found by Heurico 1.16 in 29.1 seconds.