The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1  1  1  X  X  1  1  1  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X X^2  X X^3+X^2  0 X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^2 X^2  0 X^2
 0  0  X  X  0 X^3+X^2+X X^2+X X^3  X X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X  X X^2 X^3 X^3+X^2 X^2+X X^3+X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2  0 X^2 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^3 X^3+X^2  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+85x^16+208x^17+401x^18+688x^19+1360x^20+714x^21+354x^22+160x^23+87x^24+20x^25+13x^26+2x^28+2x^29+1x^32

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.