The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  1  1  0  1  1 X^3+X^2
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X X^3+X  0 X^3 X+1  1 X^3+X^2 X^3+X^2+X+1  1
 0  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3
 0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3

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+225x^20+128x^21+320x^22+128x^23+217x^24+3x^28+2x^32

The gray image is a linear code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.16 in 0.218 seconds.