The generator matrix

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

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+96x^14+912x^15+2951x^16+11670x^17+27909x^18+54552x^19+64675x^20+56712x^21+27738x^22+10920x^23+2922x^24+878x^25+161x^26+32x^27+11x^28+4x^29

The gray image is a linear code over GF(2) with n=160, k=18 and d=56.
This code was found by Heurico 1.16 in 104 seconds.