The generator matrix

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

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+42x^16+74x^17+239x^18+378x^19+613x^20+380x^21+199x^22+52x^23+45x^24+10x^25+9x^26+2x^27+3x^28+1x^30

The gray image is a linear code over GF(2) with n=160, k=11 and d=64.
This code was found by Heurico 1.16 in 0.032 seconds.