The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+30x^20+192x^22+30x^24+2x^28+1x^32

The gray image is a linear code over GF(2) with n=176, k=8 and d=80.
This code was found by Heurico 1.16 in 1.05e-007 seconds.