The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  1  1  1  1
 0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3
 0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3
 0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+4x^18+116x^20+4x^22+1x^24+2x^28

The gray image is a linear code over GF(2) with n=160, k=7 and d=72.
This code was found by Heurico 1.16 in 6.87e-008 seconds.