The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1 X^2  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3  0  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  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+39x^16+96x^18+64x^19+639x^20+64x^21+80x^22+24x^24+16x^26+1x^36

The gray image is a linear code over GF(2) with n=160, k=10 and d=64.
This code was found by Heurico 1.16 in -6.48e-008 seconds.