The generator matrix

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

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+55x^16+162x^17+465x^18+876x^19+1012x^20+862x^21+459x^22+128x^23+48x^24+14x^25+3x^26+4x^27+4x^28+2x^29+1x^30

The gray image is a linear code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.062 seconds.