The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 X^2 X^2  1  1  1
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3  0  0 X^2 X^3+X^2 X^3  0  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3  0 X^2 X^2  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  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+35x^16+40x^17+95x^18+152x^19+372x^20+168x^21+116x^22+8x^23+8x^24+16x^25+12x^26+1x^34

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 3.81e-009 seconds.