The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X  1  1 X^3+X^2  1  1 X^3+X^2+X  X  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^2+X+1 X^3  1 X^3+X X^2+1  1 X^3+X^2  1  1 X^3+X^2+X X+1  1  0  0
 0  0 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3  0 X^3  0 X^2 X^3 X^3+X^2  0 X^2  0  0
 0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 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+45x^16+148x^17+446x^18+1004x^19+826x^20+1024x^21+428x^22+112x^23+22x^24+12x^25+22x^26+4x^27+2x^28

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 0.063 seconds.