The generator matrix

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

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+80x^17+148x^18+314x^19+895x^20+296x^21+148x^22+68x^23+34x^24+8x^25+8x^26+2x^27+1x^36

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 0.016 seconds.